Rožić played for the Croatian side Hajduk Split from 1972 to 1984. In 1984 Rožić left for Australia, where he played for the Croatian emigrant club Sydney Croatia. Upon the introduction of a multi-party system in Croatia with Communist Yugoslavia, Rožić returned in 1990 and joined the Croatian Democratic Union.
Rožić has served as mayor of Trogir. He entered the Croatian Parliament as a member of the Croatian Democratic Union in 2008 after the death of representative Ante Sanader.