First, I want to address the framing of your question.

No, the US was not responsible for the Holocaust, nor was it responsible for Nazism. The culpability for that lays solely with Germany. It was not the United States that sent Jews to concentration camps, nor was it them that systematically murdered six million Jews and several million more Romani, homosexuals, political dissidents, and many more. It would be absurd to blame that on the United States; it was, and remains, exclusively the fault of Germany.

It is important to note that, before explicit confrontation between the two powers began, the Nazis viewed the United States (and, indeed, Britain) as its racial brothers. Both were "Nordic nations", and viewed as racially superior to Slavs and Jews (though, of course, this was not uniform; the Nazis despised New York City, which they viewed as too "Jewish" for their liking.) Yet before they were in conflict, the Nazis were actually rather fond of the United States. To quote a Nazi history book, "The most important event in the history of the states of the Second Millennium - up until the [First World] War - was the founding of the United States of America. The struggle of the Aryans for world domination received thereby its strongest prop." Of course, this relationship would eventually sour, but it provides an important background for understanding American influence on Nazi ideology.

It is widely accepted that Nazism most certainly drew examples from the United States. Take the concept of lebensraum, or living space. The idea behind this was that it was the natural right of the Germans to invade eastern Europe and exterminate or enslave its native populations, with the available land being colonized by the "superior" German race. In many cases, this policy was directly contrasted with the American policy of Manifest Destiny; Hitler in 1928, for instance, expressed admiration with how the U.S. had "gunned down the millions of Redskins to a few hundred thousand, and now keep the modest remnant under observation in a cage..." This is one of many quotes from both Hitler and leading Nazi officials comparing their planned expansion in the east to American expansion westward, and indeed Hitler proclaimed that the Volga River would be the German Mississippi. However, once again, it should be emphasized that this does not mean the United States was responsible for the concept of lebensraum, but rather that its expansion served as a model that the concept was based on.

Similarly, many of the initial laws in the German Reich were drawn from American sources. The Nuremberg Laws of 1935 are a noteworthy example - they were one of the most major pieces of race legislation passed in the Nazi period, and many were drawn in part from American race legislation, especially those against miscegenation (racial intermarriage) and those concerning citizenship and the rights it entailed. Many leading Nazis praised Jim Crow and its de facto disenfranchisement of the Black population in the U.S. So too they praised U.S. immigration law, particularly the Immigration Act of 1924, which acted, in effect, to ban many potential immigrants on what was essentially the basis of race. The Nuremberg Laws drew, largely indirectly, from these laws - limiting German citizenship to those of "German blood", and banning marriage and other relations between Germans and Jews.

What cannot be said is that the United States was responsible for the Holocaust. But it was certainly an inspiration for the laws and ideologies that would lead the Holocaust to its fruition. Though I've listed several ways in which the Nazis drew on American concepts, there were also many areas in which the Nazis drew from other sources ("Who, after all, speaks today of the annihilation of the Armenians?") as well as developing new "innovations" in brutality and genocide on their own.

Source:

Hitler's American Model: The United States and the Making of Nazi Race Law by James Q. Whitman

Source for the Armenian Genocide quote:

https://www.armenian-genocide.org/hitler.html