Auld was born in Maryhill, Glasgow. He first joined Celtic in March 1955 from local side Maryhill Harp, where he was converted from a fullback into a winger. However his headstrong character and poor discipline impeded his progress and after spending a season on loan to Dumbarton, he was sold to Birmingham City in 1961 for £15,000. With the Midlands club he won a League Cup medal in 1963, as well as appearing in the final of the 1960–61 Inter-Cities Fairs Cup, in which Birmingham were beaten 4–2 on aggregate by A.S. Roma.
In 1965 Auld returned to Celtic in a £12,000 deal, possibly on the initiative of Jock Stein, who had not yet been appointed Celtic manager. No longer considered a winger, Auld formed a midfield partnership with Bobby Murdoch. He became an integral part of the side that won nine League titles, as well as the 1967 European Cup Final. Prior to that match, against Italian giants Internazionale, Auld instigated a rendition of The Celtic Song in the tunnel, much to the bemusement of the Inter players. Auld left Celtic again in 1971 this time joining Hibernian on a free transfer. While at Easter Road he combined his playing role with one as a trainer, eventually focusing solely on the latter role.