Prevent Russian Infiltration Act of 2013 - Prohibits the Secretary of State from approving a Russian space agency (Roscosmos) request to build or operate a ground monitoring station in the United States, including in any U.S. territory or possession, until the Secretary, the Secretary of Defense (DOD), and the Director of National Intelligence jointly certify to Congress that any such proposed station does not raise counterintelligence or other national security concerns.