Robert Alexander Rankin (27 October 1915 – 27 January 2001) was a Scottish mathematician who worked in analytic number theory.

Rankin's father, the Revd Oliver Shaw Rankin, was a minister who later became Professor of Old Testament Language, Literature and Theology in the University of Edinburgh.

Rankin was born in Garlieston, Wigtownshire, Scotland, attended Fettes College and graduated from Clare College, Cambridge, in 1937. In Cambridge he was particularly influenced by J.E. Littlewood and A.E. Ingham.

He was elected a fellow of Clare College in 1939, but his career was interrupted by the Second World War, during which he worked on rocketry research at Fort Halstead. In 1945 he returned to Cambridge, and then moved to the University of Birmingham in 1951 as Mason professor of mathematics. In 1954 he became Professor of Mathematics, Glasgow University, retiring in 1982.

In 1987 Rankin received the Senior Whitehead Prize from the London Mathematical Society.

He had a continuing interest in Srinivasa Ramanujan, working initially with G.H. Hardy on Ramanujan's unpublished notes. His research interests lay in the distribution of prime numbers and in modular forms; he developed what is now known as the Rankin – Selberg method in 1939.

He died in Glasgow in 2001.