Ayr born goalkeeper Willie Muir began his football career with Glenbuck Athletic in 1894 before joining Scottish League Third Lanark in 1895. He moved to Kilmarnock in 1896 and spent a year at Rugby Park before heading south to join First Division Everton in 1897. He made his Football League debut at West Bromwich Albion that November, taking over the no.1 berth from Rab MacFarlane, and he was in goal for their 1898 FA Cup semi final defeat to Derby County at Molineux. He eventually lost his place in The Toffees’ goal to George Kitchen in October 1901, and having made 137 appearances he returned to Scotland in 1902 to join Dundee.
While at Dens Park he helped them to runners up position in the Scottish League in both 1902-03 and 1906-07. In both seasons representative honours followed – he first represented The Scottish League in March 1903 when he played in a 3-0 defeat to The Football League at Parkhead. But he was recalled to The Scottish League line-up in March 1907, playing against The Football League in a 0-0 draw at Ibrox. Two weeks later he was awarded a full Scottish international cap when he kept goal in a 3-0 victory over Ireland at Parkhead.
In the 1907 close season he returned to England to join Second Division Bradford City and played 30 times as they won the 1907-08 Second Division Championship, however after only one season for The Bantams he returned to Scotland and joined Heart of Midlothian, where he made 66 appearances over the following two seasons. In 1910 he joined Dundee Hibernian, before finishing his career with Dumbarton joining them in 1911, where he made 8 appearances, his final career appearance being in a Scottish Cup tie defeat to East Stirlingshire in January 1912.