Galashiels born outside right Willie Kivlichan played junior football for Dumfries St Joseph’s in 1902, Maxwelltown Juniors in 1903, and Dumfries in 1904, also playing for Glasgow University, before joining Rangers as an amateur in 1905. He made his debut for Rangers at Motherwell in November 1905 and scored 7 goals in 20 appearances during his two seasons at Ibrox, which included scoring a winning goal for the Ibrox club against their bitter rivals Celtic, before joining Celtic in May 1907 in a swap deal for Alex Bennett, a Protestant then playing for Celtic, while Bivlichan was a Catholic playing for Rangers. He netted twice on his debut as Celtic won a Scottish League encounter at Morton 3-2 on August 24th 1907. Then in February 1908 the Glasgow University student hit another double to defeat Rangers 2-1 at Ibrox in the Scottish Cup.
He helped Celtic to three successive Scottish League titles in 1908, 1909 and 1910, and represented The Scottish League 3 times between October 1909 and October 1910, playing twice against The Irish League and once against The Southern League. He then departed Parkhead in April 1911 to Second Division Bradford Park Avenue to play under Tom Maley. He had played 92 League & Scottish Cup games for the Bhoys and scored 22 goals. He made his Football League debut at Birmingham in September 1911 and soon became a regular feature in the Avenue team. At Bradford he helped the club to promotion to the First Division in 1914 and scored 5 times in 96 appearances before the First World War interrupted his career.
During the First World War, Kivlichan served as a lieutenant in the Royal Army Medical Corps, attached to the King’s Own African Rifles. He was seriously injured in August 1918 but recovered from his wounds. After the War he qualified in medicine from the University of Glasgow, and played for Queen of the South.
Kivlichan subsequently became the Celtic team doctor. He was by the side of John Thomson as the young Celtic goalkeeper tragically died from a head injury sustained in an Old Firm match on 5th September 1931.