WASHINGTON—Jerome Corsi, a conservative author and activist best known for advancing conspiracy theories about former President Obama’s birthplace, said he expected to be indicted in the special counsel investigation into Russian interference in the 2016 election.

Speaking on a YouTube broadcast on Monday, Mr. Corsi said that he expects to be charged with giving false information to investigators working for special counsel Robert Mueller. In recent weeks, Mr. Corsi had been cooperating with investigators here.

“I fully anticipate in the next few days I will be indicted by Mueller for some form or other of giving false information to the special counsel,” Mr. Corsi said.

Prosecutors often inform potential defendants that they will be indicted or charged, a move that can lead to discussions over plea agreements or further cooperation.

Mr. Corsi didn’t say why he believed he would be indicted, but he has appeared before a grand jury in recent weeks, and prosecutors are encouraged to tell witnesses of their legal exposure.

On his live broadcast, Mr. Corsi said: “Criminals are running the Department of Justice. I think my crime really was that I dared to support Donald Trump.” He also asked for donations to help pay his legal bills.

Mr. Corsi said that he had turned over his computers and phone records to investigators in an effort to cooperate and demonstrate that he had nothing to hide. Mr. Corsi was also questioned by investigators about his interactions with other conservative activists and the website WikiLeaks before a grand jury, The Wall Street Journal previously reported.

“We had nothing to hide," Mr. Corsi said on YouTube about his cooperation with the special counsel investigation.

Representatives for Mr. Mueller’s team didn’t immediately respond to a request for comment.

During the 2016 campaign, Mr. Corsi was also a part of a small, informal network of researchers and activists on the margins of Republican politics who were looking for incriminating information about Hillary Clinton, Mr. Trump’s Democratic rival. The Journal has previously reported that the special counsel is looking at whether Mr. Corsi or any other activists had advance knowledge of email hacks and leaks that U.S. intelligence agencies have said were part of a Russian campaign to help Mr. Trump win.

Prosecutors have been scrutinizing messages sent between Mr. Corsi and Roger Stone, a Trump confidant, in which they discussed material that would eventually be released by WikiLeaks founder Julian Assange, according to a person familiar with the matter. In his YouTube broadcast, Mr. Corsi asserted that he had “figured out” that Mr. Assange had emails from Clinton campaign chairman John Podesta.

In a statement, Mr. Stone said his correspondence with Mr. Corsi proves “everything I have said under oath regarding my interaction with Dr. Corsi is true.”

A onetime Wall Street investor turned political activist and commentator, Mr. Corsi rose to national prominence by advancing the false theory that Mr. Obama had been born in Kenya. He also has advanced unfounded theories about the Sept. 11, 2001, terrorist attacks and the existence of a “deep state” within the U.S. government bent on undermining Mr. Trump, and suggested Adolf Hitler may have escaped Nazi Germany.

During the 2016 campaign, he supported Mr. Trump, who himself popularized the “birther” theory about Mr. Obama’s birth in advance of his 2016 presidential run.

Mr. Corsi, 72 years old, said on YouTube he was worried that he would spend the rest of his life in prison, possibly in solitary confinement. However, federal sentencing guidelines for offenses similar to that which Mr. Corsi said he would be charged typically call for probation or a very short prison sentence for offenders without any prior convictions.

The role that WikiLeaks and Mr. Assange played during the 2016 election as the chief publisher of stolen Democratic emails has been of enduring interest to investigators probing Russian election interference in 2016 and allegations of collusion between Moscow and Trump associates.

Mr. Trump has denied collusion, and Moscow has denied interference in the election. The Mueller probe has resulted in more than two dozen indictments, as well as guilty pleas by five Trump associates.

Write to Byron Tau at byron.tau@wsj.com