Rosetta was born in Vercelli, Piedmont, where he debuted for Pro Vercelli in the Italian First Division (Serie A's predecessor) in the 1919-20 season, as a striker. He later turned into an effective defender.
Pro Vercelli was then one of the major Italian football teams, and Rosetta won two scudetti in 1921 and 1922. He debuted for Italy at the 1920 Summer Olympics, forming a partnership with Renzo De Vecchi.
In 1923 he moved to Juventus, where he was paid as a footballer for the first time. He won his first title in 1926, and was an integral part of the team which won five consecutive scudetti during the 1930s.
He was a member of the Italian football team, which placed fifth at the 1924 Summer Olympics and won the bronze medal at the 1928 Summer Olympics.
He won a total of eight national championships, with the final five being Serie A titles. Only two players, Giovanni Ferrari and Giuseppe Furino, have also won eight titles in the Italian leagues.
For Italy, Rosetta received a total of 52 caps, and he was a member of the 1934 FIFA World Cup winning squad. He was captain in Italy's first game at the tournament, but it proved to be his last international appearance and he did not play in the final itself. He retired in 1936.
He died in Turin in 1975.