From an earlier answer of mine and be sure to look at /u/The_Alaskan 's answer as well.

Although the US and Russia enjoyed largely cordial and at times quite friendly relations for a goodly part of the nineteenth century, the relations between the Republic and the Empire had begun to chill from the assassination of Tsar Alexander II and remained somewhat frosty through the fall of the Romanovs in 1917. Although relations never broke into open hostility, there were multiple problems US policymakers had with both the Romanov's autocracy and its various policies.

The assassination of Alexander II sparked a series of anti-Jewish pogroms and these would reoccur periodically throughout the empire's remaining lifespan. The pogroms encouraged the emigration of Russian Jews to the US, a development that caused a great alarm in some circles of American policymakers. President Benjamin Harrison's December 1891 message to Congress registered the American government's "serious concern" over the:

harsh measures now being forced against Hebrews in Russia, prompting great numbers of these unfortunate people By the revival of anti-Semitic laws, long in abeyance, great numbers of those unfortunate people have been constrained to abandon their homes and leave the empire by reason of the impossibility of finding subsistence within the Pale to which it is sought to confine them. The immigration of these people to the United States- many other countries being closed to them- is largely increasing and is likely to assume proportions which may make it difficult to find employment for them here and to seriously affect the labor market. It is estimated that over one million will be forced from Russia within a few years.

Although Harrison's concern over these "one million" refugees masked a degree of antisemitism as well, the pogroms became a major sticking point in Russian-American relations. Jewish political pressure groups, first led by assimilated German-American Jews and later by the newly established Eastern European-Jewish enclave began to exert pressure both on Congress and the President to more forcefully protest anti-Jewish violence in the Pale. The fact that this Jewish demographic settled in major urban centers gave these pressure groups a degree of political heft. The 1892 Democratic platform called for Russia to stop repressing its Jewish ad Lutheran minorities. The particularly brutal Kishinev pogrom in 1905 prompted a very vocal note of protest from American government officials. Former President Grover Cleveland spoke against Russian actions in Carnegie Hall and President Teddy Roosevelt wrote a telegram directly to the Emperor protesting the Romanov's apparent countenancing of the pogrom.

While this protest was a Rubicon for American condemnation of human rights abuses, it also came in the context of increasing tensions over Russian treatment of American nationals in the Empire. The 1832 commercial treaty between the two countries established a pattern for passports and freedom of movement of nationals. With the ascension of the autocratic and arch-conservative Emperor Alexander III after his brother's assassination, the Russian Interior Ministry began to clamp down on passport regulations. Although this increased regimen of passport regulation was directed against the Empire's various subjects, they did restrict the freedom of movement of American nationals in the Empire, especially if they were of Jewish extraction (for the most part, most Russian Jews were legally prevented from leaving the Pale unless they were professionals). Although US Presidents tried to use persuasion and soft power to modify Russian behavior, such efforts accomplished very little and under the leadership of Senator Henry Cabot Lodge, Congress abrogated the Treaty in 1911 because of mounting pressure from Jewish pressure groups like National Citizens Committee for Abrogation.

Yet the Empire's atrocious record on the treatment of its Jews was not the only cause of the deterioration of Russo-American relations. The emerging American radical press was one of the venues available for Russian political exiles and helped undercut the Romanov's pretenses to be a uniquely holy monarchy. The explorer and public intellectual George Kennan (a cousin of the famous diplomat) wrote a highly influential expose of the Russian penal system, Siberia and The Exile System in 1891 which highlighted the inhumanities of Russia's system of exile and police supervision. Russian expansion in the Far East also flew in the face of America's sponsorship of the Open Door for China.

These attitudes led to a perceptible tilt against Russia in American foreign relations. Although American enthusiasm for Japan's victory over Russia dimmed when it became apparent of the scale of Japan's victory, President Theodore Roosevelt had a clear bias against Russia in 1905. The American government's reactions to the 1905 Revolution was muddled and confused, much like the Revolution itself, but the US government noted its approval of the Romanov's adaption of a constitution and the Duma. Such sentiments reflected a growing sense that the Romanov's autocratic ruling methods were antithetical to American ideas of democracy. Mark Twain, for example, initially wrote rather warmly about the Russia in the 1870s, but his opinion on the Romanovs had clearly soured by the 1890s. In an 1890 unsent letter to the periodical Free Russia, the American writer noted with characteristic wit:

Of course I know that the properest way to demolish the Russian throne would be by revolution. But it is not possible to get up a revolution there; so the only thing left to do, apparently, is to keep the throne vacant by dynamite until a day when candidates shall decline with thanks. Then organize the Republic. And on the whole this method has some large advantages; for whereas a revolution destroys some lives which cannot well be spared, the dynamite way doesn't. Consider this: the conspirators against the Czar's life are caught in every rank of life, from the low to the high. And consider: if so many take an active part, where the peril is so dire, is this not evidence that the sympathizers who keep still and do not show their hands, are countless for multitudes? Can you break the hearts of thousands of families with the awful Siberian exodus every year for generations and not eventually cover all Russia from limit to limit with bereaved fathers and mothers and brothers and sisters who secretly hate the perpetrator of this prodigious crime and hunger and thirst for his life? Do you not believe that if your wife or your child or your father was exiled to the mines of Siberia for some trivial utterances wrung from a smarting spirit by the Czar's intolerable tyranny, and you got a chance to kill him and did not do it, that you would always be ashamed to be in your own society the rest of your life? Suppose that that refined and lovely Russian lady who was lately stripped bare before a brutal soldiery and whipped to death by the Czar's hand in the person of the Czar's creature had been your wife, or your daughter or your sister, and to-day the Czar should pass within reach of your hand, how would you feel -- and what would you do? Consider, that all over vast Russia, from boundary to boundary, a myriad of eyes filled with tears when that piteous news came, and through those tears that myriad of eyes saw, not that poor lady, but lost darlings of their own whose fate her fate brought back with new access of grief out of a black and bitter past never to be forgotten or forgiven.

Twain's letter captured some of the ambivalence about Russo-American relations during the fin de siècle; many Americans were alarmed by Russian actions, but saw no easy solution as these events became increasingly connected to Tsarist autocracy. The rub was there was no clean and easy way to remove the Romanovs from power. Although American business concerns like Singer were making their presence known in Russia, Hollerith punchcard machines helped make the 1897 all-Russia census possible, these enterprises were still only a small proportion of American foreign trade, which gave human rights concerns a degree of power. Thus while Russo-American relations had been exceptionally good over such matters as boundary areas and there were periodic signs of rekindling the cordial relations of the early nineteenth century, the two nations were at increasing loggerheads prior to the February Revolution of 1917.

Sources

Healy, Ann E. "Tsarist Anti-Semitism and Russian-American Relations." Slavic Review 42, no. 3 (1983): 408-425.

Mayers, David. "History of Russian-US Relations, 1867–1921." Diplomatic History 27, no. 3 (2003): 409-414.

Saul, Norman E. Concord and conflict: the United States and Russia, 1867-1914. Topeka: University Press of Kansas, 1996.