Torriani served as the Switzerland national team captain from 1933 to 1939. He played on a forward line known as "The ni-storm" (), with brothers Hans Cattini and Ferdinand Cattini. The line was named for the last syllable ("-ni") of players' surnames. The ni-storm was regarded as the top line of HC Davos and Switzerland's national hockey team from 1933 to 1950. On this line, he scored five goals in six games at the 1933 Ice Hockey World Championships, 14 goals in seven games at the 1934 World Ice Hockey Championships, and eight goals in eight games at the 1935 Ice Hockey World Championships. Torriani led Switzerland to a silver medal at the 1935 championships, and a bronze medal at the 1939 Ice Hockey World Championships. He also competed in ice hockey at the 1936 Winter Olympics, playing in three games with no goals scored.