Assange is currently fighting extradition to Sweden and is awaiting a decision from the British Supreme Court. He has repeatedly denied the sexual assault claims against him, saying they are politically motivated.
The 40-year-old Australian citizen has criticized the prime minister for not standing up for him against the potential threat of his extradition to the U.S. over the release of classified documents. Prime Minister Julia Gillard called the action "grossly irresponsible."
The next Senate election cannot be called before July 2013 and is due around August. Candidates cannot officially register as candidates until the election is called at least a month before the poll date.
WikiLeaks said it would also be running a candidate against Gillard.
The Associated Press contributed to this report.