Chelsea Manning was originally sentenced to 35 years imprisonment but had her jail time significantly shortened following an intervention from former president Barack Obama.
Ms Manning, formerly known as Bradley Manning, would be challenging Democrat Ben Cardin, who has already served two terms in the Senate and faces re-election in November.
A federal election filing, made on Thursday, confirmed Manning’s intention to run in the November elections, according to the Washington Post.
Ms Manning was released from Fort Leavenworth military prison, in Kansas, in May 2017, after spending a total of seven years in custody.
She was imprisoned after being found guilty of sharing more than 700,000 documents, videos and battlefield accounts with the anti-secrecy group, founded by Julian Assange.
The ex-intelligence analyst acknowledged leaking the materials and said it was an attempt to expose what she believed was the US military’s apparent disregard for the effects on civilians.
She became known around the world for her actions but was condemned for sharing some of the country’s most sensitive secrets and endangering sources, many of whom had to be moved.
Incumbent US president Donald Trump has previously criticised MS Manning, calling her an “ungrateful TRAITOR…who should never have been released from prison” in a characteristically combative tweet.