After growing up in Torino's youth sector, Tagnin was later promoted to the club's senior side, but began his professional career during the 1952–53 season, on loan to his hometown club Alessandria, in Serie C. He returned to Torino the following season, and remained with the club until 1954, making his Serie A debut with the club in a 1–1 away draw against Sampdoria, on 13 September 1953. He later also played for Monza in Serie B (1954–57), briefly returning to Alessandria for the 1957–58 Serie A season. Tagnin subsequently played for Lazio (1958–59), where he won the Coppa Italia in 1958, and Bari (1959–61), but was subsequently banned for two and half seasons after being accused of being involved in a gambling scandal. His sentence was later reduced by a year, and in 1962, he joined Internazionale, where he had his most notable spell, remaining with the club until 1965, after struggling to gain playing time ahead of the younger defensive midfielder Gianfranco Bedin during his final season with the team. Tagnin ended his career after the 1965–66 season, returning to Alessandria once again, in Serie B.