Rašović started to play in Partizan youth teams. He played professionally, initially, with FK Rad and Bulgarian Slavia Sofia. Then he returned to FK Partizan where he played from 1998 to 2002. In 2002, he moved to Krylia Sovetov of Russia, where he played between 2002 and 2003. In 2004, he signed with the American MLS team Kansas City Wizards but only played in one game for them during the 2004 season. He retired after the year after suffering an injury.