Menzies was a player at Raith Rovers where his father was chairman. In 1903 he joined newly formed English side Bradford City as a reserve player. He also served as a steward and trainer until the outbreak of World War One. In July 1916 he began his managerial career at Hull City following two years as trainer at the club. He served for two seasons in post-war football leading the club to a mid-table position in Division Two.
In July 1921 he returned to Bradford City to take over from Peter O'Rourke. O'Rourke had helped City to lift the FA Cup and kept City in Division One for nine successive seasons giving Menzies a difficult task to follow. City were relegated in Menzies' first season. For four more seasons the club struggled in the bottom half of Division Two and Menzies resigned in June 1926.