Stinčić, son of Yugoslav international Branko Stinčić, started playing at NK Dinamo Zagreb in 1967, but had only a handful of appearances in his first six seasons with the club, acting as a secondor third-choice goalkeeper at the time when established goalkeepers Zlatko Škorić and Fahrija Dautbegović were at the club
By 1981 he played a total of 478 games (including 190 league matches) for the Blues. At the end of the 1980-1981 season he moved abroad to Austrian side SV Austria Salzburg, where he played for four seasons, appearing in 91 Austrian Bundesliga games, before retiring in 1985. He was capped once for Yugoslavia, in an Euro 1980 qualifier against Spain on 4 October 1978 and conceded two goals from Juanito and Santillana in a 2–1 defeat.
After retiring he worked as a goalkeeping coach at Dinamo Zagreb until 2005, when he opened a goalkeeping academy together with Zlatko Škorić.
Following Dautbegović"s departure, Stinčić appeared in 21 Yugoslav First League matches in the 1973-1974 season, and became a regular member of the first team squad in the following years.
