Muirhead has previously played for Annan Athletic, Partick Thistle and Falkirk, after progressing through Ayr United's youth academy.

Muirhead started his career with Ayr United's youth academy, before signing for Annan Athletic in November 2008, going on to play in 127 matches and scoring 15 goals.

[7] Muirhead also scored a penalty in the Scottish League Cup win versus Cowdenbeath as the Harry Wraggs won 3-1 after extra time.

[14] Following the conclusion of the 2023–24 season, Muirhead triggered an appearance based contract extension, which added a year to his Thistle deal.

[15] In February 2025, Muirhead joined Scottish League One side Arbroath on loan until the end of the season.