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's Rangers career was interrupted by a brief stint in the US in 1925. Cash-rich American Soccer League club Boston Soccer Club lured him across the Atlantic to assume the role of player-manager. However, despite the presence of several other Scots, including internationalists such as Alex McNab and Barney Battles, he could not settle in Boston and returned to Glasgow after only 14 games.