The claim came shortly after it was reported that a teenaged hacker had broken into the US spymaster's AOL account and had taken mails and personal data.
The FBI and Secret Service are investigating the claims, which, if true, would be a major humiliation for US intelligence after a string of major leaks.
"ANNOUNCE: We have obtained the contents of CIA Chief John Brennan's email account and will be releasing it shortly," the @Wikileaks Twitter account said.
The account has been verified by Twitter as belonging to the organization and is widely assumed to be controlled by Wikileaks' founder Julian Assange.
Earlier this week the New York Post reported that a hacker, who described himself as an American high school student, had called reporters to describe his exploits.
He claimed Brennan's private email account held sensitive files, including his 47-page application for security clearance.
Then, using his purported Twitter account -- @phphax -- the hacker taunted authorities with redacted images of what appeared to be government information.
The Twitter account claims the hacker is 13 years old, and expresses support for the Palestinian cause.
Senior officials have also been criticized for not properly protecting sensitive and classified documents.
Former CIA chief David Petraeus was forced to plead guilty to improperly handling documents after it emerged that he loaned his mistress his Afghan war diaries.
And presidential candidate Hillary Clinton is under fire after she admitted that she only used a private email server during her time as Secretary of State.
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