Born with the surname Urbonis,[1] Millar was a member of North Lanarkshire's Lithuanian immigrant community.[3][4] After playing with several local Junior teams until the age of 23, he began his senior career with Celtic in 1935,[5] where he was a reserve behind Willie Lyon in the queue for selection; he made five appearances as the club won the 1937–38 Scottish Division One title, but it is doubtful that he would have been presented with a medal. With the situation unchanged going into the following campaign he moved on, joining Preston North End in October 1938.[4] He had little time to become established in English football prior to the outbreak of World War II ten months later, and during the conflict he appeared as a guest player for Scottish clubs including Celtic and Motherwell, featuring for the latter in the 1945 Southern League Cup Final which ended in defeat by Rangers.[6][7]
In 1946 Millar signed for Scottish Division B side Dundee United,[8] transferring back up to the top tier with Morton in late 1947 and playing for them in the 1948 Scottish Cup Final – again losing out to Rangers, this time after extra time in a replay; his performance in both matches against his internationalist opponents Billy Williamson and Willie Thornton, at the age of 36, was singled out for particular praise in press reports.[9][10] After Morton were relegated in the 1948–49 season, he moved on to Stranraer for a short spell prior to retiring.[11]
Millar also served as chairman of the Scottish Football Players Union in the post-war period.[4][12] He was the first of several Scots of Lithuanian descent to play for Celtic between the 1930s and 1960s, all of them defenders, the most famous being Billy McNeill.[4][13]