Yes, though maybe not the type of "conspiracy theory" you're thinking of.

To start with, there actually was a conspiracy and it involved John Wilkes Booth, Lewis Powell, Mary Surratt, David Herold, and George Atzerodt. Booth died while on the run, while the others were all executed for it. There was also the various involvement of Edmund Spangler, Samuel Mudd, Samuel Arnold, and Michael O'Laughlen, who were all imprisoned for their roles. The son of Mary Surratt, John, was also arrested and tried but it resulted in a mistrial and the U.S. government dropped the case.

From the testimony and verdicts in the various trials, the U.S. government proved that Lincoln was assassinated by John Wilkes Booth, Secretary of State William Seward was stabbed by Lewis Powell but survived, while Andrew Johnson went unscathed when George Atzerodt failed to go through with the assassination attempt he had agreed to carry out.

The conspiracy beyond the actual conspiracy was that Booth and friends weren't just a group of rogue agents, but that the assassination was ordered by the higher-ups of the Confederate government.

The Confederates had formed a spy organization called the Confederate Secret Service, which stationed secret agents in Canada to sneak into the North and carry out plots against the Union government and military.

The Confederate Secret Service was led by Jacob Thompson and Clement C. Clay, Jr. Thompson had been the Secretary of Interior under President James Buchanan, and resigned after secession started, becoming the Inspector-General of the Confederate Army. Clay was a Senator from Alabama who joined secession when Alabama did.

In November 1864, Thompson ordered a group of Confederate Secret Service agents to carry out a plot in New York City in which the agents would book hotel rooms in various parts of the city, then set fire to those hotels, in the hopes of burning the city down. Most of the attempted fires fizzled out, and most of the agents escaped back to Canada, except one who was tried, convicted, and then executed in February 1865.

Investigators pursued whether or not the assassination had any connection to the Confederate Secret Service's actions, as had become apparent with the New York plot. There was no FBI or CIA back then, so the investigation into Lincoln's assassination was essentially led by Secretary of War Edwin Stanton. The investigation turned up evidence that Booth had worked with the Confederate Secret Service, and had gone to Canada and met with agents there. The U.S. government suspected that the Booth assassination had perhaps been ordered by Senator Clement Clay in his role with the Confederate Secret Service.

President Andrew Johnson signed an arrest warrant for Clay, who turned himself in. He spent about a year in jail, from May 1865 until April 1866.

Edwin Stanton also issued an indictment for the assassination of Abraham Lincoln against Confederate President Jefferson Davis. For that crime and others, Davis was captured, and put in jail, also for about a year, from May 1865 until May 1866.

Jacob Thompson, who was in Canada at the end of the war, slipped away to England and spent time hiding out there before coming back to Canada to hide again.

On December 25, 1868, President Andrew Johnson issued a general pardon for all persons engaged with the Confederacy which let Davis, Clay, and Thompson off the hook, so neither Davis or Clay was ever tried in connection with the assassination of Abraham Lincoln. This also allowed Thompson to re-enter the country without having to face prosecution.

So there were formal accusations by the U.S. government that the conspiracy went further than Booth and his friends, involving elements from the Confederate government. But since the pardon was granted, this conspiracy theory was never pursued at trial.

Since there was no FBI or CIA or Secret Service yet, they couldn't be accused of a "conspiracy". Lincoln did have four bodyguards that night, and one of them, John Parker, was tried for dereliction of duty, but the case was dismissed.

None of the members of Lincoln's Cabinet were accused of a "conspiracy" since they were also intended victims of the actual Booth conspiracy.

A member of Congress was accused of a "conspiracy", namely the aforementioned Clement Clay, Senator from Alabama.

And a foreign citizen was also accused of a "conspiracy", namely George Atzerodt who failed to kill Andrew Johnson and was hanged for his role in the plot.

Later study has made it clear that Clay, Davis, and the Confederate government almost certainly had no foreknowledge of Booth's actions that night. Booth had gone to Ford's Theater that day to check his mail and a stagehand, Edmund Spangler, told him Lincoln would be attending that evening's performance. This set the conspiracy in motion. At best, Booth may have met Clay in Canada much earlier and been given a general order to kill Lincoln if the opportunity arose, but Clay wouldn't have known anything specific of the actual conspiracy that unfolded. Davis would have known even less, and by all accounts, it wouldn't have been in his nature to order such an attack. He publicly lamented the assassination, saying, "For an enemy so relentless in the war for our subjugation, we could not be expected to mourn, yet, in view of its political consequences, it could not be regarded otherwise than as a great misfortune for the South.”

In short, there were accusations of a conspiracy involving the wider Confederate government, but this was not pursued once President Andrew Johnson pardoned all members of the Confederacy in 1868. Later research never turned up any credible evidence that anybody beyond Booth and his co-conspirators were involved.

The earliest sort of "conspiracy theory" that you're probably thinking about holds that the Catholic Church did it. Beginning in the 1880s, some books were being published that were anti-Catholic conspiracy rags in general, and some mentioned that the Lincoln assassination was a Catholic plot, through accused co-conspirator John Surratt who was Catholic. The earliest mention comes from 1886 book Fifty Years In the Church of Rome which includes the passage:

"...[A]fter twenty years of constant and most difficult researches, I come fearlessly today before the American people, to say and prove that the president, Abraham Lincoln, was assassinated by the priests and the Jesuits of Rome."

This was written by a guy named Charles Chiniquy. He advances the theory that word was given of the assassination at the Catholic Church in St. Joseph, Minnesota, hours before the actual assassination took place. Taken at his word, he had been researching the conspiracy since 1866. Was this his own invention or was this indicative of 1860s thought?

Chinquy was the first to write of the conspiracy, but not the last. 1888's Washington In the Lap of Rome, and 1895's America or Rome? Christ or the Pope? both reprinted the conspiracy, the former citing Chinquy as its source. Another book from 1895 contains this passage:

"The assassination of Lincoln, a man who is the more admired the better time makes him known, filled the land with dismay and indignation. An attempt was made to lay the deed to the charge of the Catholics...John Surratt, a Catholic, misled by his Southern sympathies, was implicated..."

Perhaps there were some rumors back in the 1860s and 1870s. There was certainly a lot of anti-Catholic sentiment in 19th Century America, so it wouldn't be surprising. Then again, it could have been the invention of Charles Chinquy. In either case, Chinquy certainly is responsible for spreading it through the written word, which other anti-Catholic writers picked up on in the 1880s and after.

SOURCES:

The Life, Crime, and Capture of John Wilkes Booth, with a Full Sketch of the Conspiracy of Which He was the Leader by George Alfred Townsend, 1865

"Assassination of President Lincoln", from History Of The Plots And Crimes Of The Great Conspiracy To Overthrow Liberty In America by Deacon Smith Dye, 1866

"Report of the Judge Advocate General, November 13, 1865" from the Congessional Serial Set, 1866

Transcript of the Trial of John H. Surratt, U.S. Government Printing Office, 1867

The Assassination of Abraham Lincoln... by the U.S. State Department, 1867

"The Great American Tragedy: The Assassination of the President", (parts one and two), The Shamrock, February 1868

"The Assassination of Abraham Lincoln: What The Newspapers Said When Lincoln Was Killed", Smithsonian Magazine, by Harold Holzer, March 2015