After starting out at Hercegovina Sečanj, Rnić briefly played for Proleter Zrenjanin, before moving to Crvenka. He later returned to Proleter Zrenjanin. In 1986, Rnić moved abroad to TV Niederwürzbach.
International career
At international level, Rnić represented Yugoslavia and competed in three Olympic Games, winning the gold medal in 1984 and the bronze medal in 1988. He also participated in two World Championships, winning the 1986 edition.