Runciman trained at the Foulis Academy, Glasgow, and was later apprenticed to the landscape painter Robert Norie, alongside working as a stage painter in Edinburgh.
In 1767, he went to Rome, where he developed an appreciation for historical and imaginative subjects, to which he began to turn his brush. Upon his return from Italy he settled in Edinburgh, and was appointed master of the Trustees' Academy. He was patronised by Sir James Clerk, whose hall at Penicuik House he decorated with a series of subjects from Ossian, later destroyed in a fire.
He enjoyed a strong reputation as a landscape painter throughout his life, and died in Edinburgh in 1785.