Muirhead, a forward who was occasionally deployed as a half-back, was signed by Rangers for £20 from Hibernian in May 1917. He made his debut against his former club in a 3–0 win at Ibrox on 15 September 1917, although he did not become a regular until the following season.
Muirhead returned to Rangers where he played until 1930. He scored 46 goals in 349 overall appearances for Rangers and won eight Scottish Football League championship medals. He was also captain of the club for a spell.
International
Muirhead was capped at international level, making eight appearances for Scotland. He captained Scotland in a 1–0 defeat against Ireland on 25 February 1928.