Bordon was born in Marghera, Venice. During his Serie A career (from 1970 to 1989) he played for Inter (1970–83); he initially served as a back-up to Lido Vieri, but later won a place as the team's starting goalkeeper, winning two Serie A titles in 1971 and 1980, as well as two Coppa Italia titles; he also reached the 1972 European Cup final with Inter, where they were defeated by Cruyff's Ajax side. He later played for Sampdoria (1983–86), where he won another Coppa Italia in 1985. He also played for Sanremese (1986–87) and Brescia (1987–89) before retiring.