Cardin was easily re-elected in 2012, beating his Republican challenger by 30 points in the heavily-Democratic state.
The seat Manning is vying for is now held by Democrat Ben Cardin, who has held it since 2007.
Manning declared her intentions January 5 with the Federal Election Commission, which posted the document on its website Thursday. Manning was released from prison in May. 1st Class Bradley Manning, a US military intelligence analyst.
President Obama commuted her sentence, and Manning was released from military prison last year after serving seven years. She was convicted by court-martial in 2013 of espionage and other offenses for furnishing more than 700,000 documents, videos and diplomatic cables to WikiLeaks, an global organization that publishes information from anonymous sources.
At the time she said she wanted to expose what she considered to be the US military's disregard for how the Iraq War was affecting civilians.
Manning leaked more than 700,000 government documents to WikiLeaks because she believed she had a responsibility to the public, she has said.
A representative for Manning did not immediately respond to a request for comment.