Glasgow born left half Alexander Torrance began his football career with Renfrew Juniors after the end of the First World War from where he joined Second Division club Bristol City in 1921, making his Football League debut at West Ham that October. He immediately established himself as a first team regular, missing very few matches for The Robins during his first three seasons. Those seasons saw Bristol City relegated to the Third Division (South), although they immediately won the Third Division (South) Championship in 1922-23, before suffering relegation once again in 1923-24.
In that 1923-24 season he missed only 4 matches, and took over penalty taking duties, scoring 4 times from the spot. However he lost his regular place in September 1926 and played only 3 more matches towards the end of the season as Bristol City were again promoted to the Second Division as Third Division (South) Champions, but Torrance only featured in five matches back in the Second Division between February and March 1928. In seven seasons at Bristol City he scored 10 goals in 176 appearances before joining non league Bath City in 1928, his final known club before his eventual retirement.