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Rasovic played professionally with Slavia Sofia of his Bulgaria in 1997. He played with Partizan Belgrade of his native Serbia from 1998 to 2002. In 2002, he moved Krylya Sovetov of Russia, where he played in 2002 and 2003. In 2004, he signed with the Wizards, but only played in 1 game for them during the 2004 season.
Rasovic has played for the Serbia and Montenegro national football team ten times, making his debut June 14, 1997 against Egypt, but has not played for them since 2001.