He was son of Thomas Creighton and Margaret Stuart, who claimed kinship with the ancient Lords of Ruthven, and was born at Dunkeld, Perthshire.
In 1625 he was made Regius Professor of Greek, and on 27 February 1627 succeeded his friend, George Herbert, as public orator of the university, holding both these offices until 1639.
He was a member of the court of Charles II in his exile, and John Evelyn (who attests to his learning) heard him preach at St. Germain on 12 August 1649, and subsequently at the Restoration at the Chapel Royal, St. Paul's Cathedral and an 'extravagant' sermon given before the House of Commons on 27 April 1663 at St. Margaret's, Westminster.
On entering on this office at the Restoration he found the deanery in the hands of Cornelius Burges, who refused to surrender it.
Creighton published Vera Historia Unionis inter Graecos et Latinos sive Concilii Florentini exactissima narratio, a translation into Latin from the Greek of Sgoropulos, the Hague, 1660, with a long preface; this was answered by the Jesuit Leo Allatius In R. Creygtoni apparatum versionem et notas, Rome, 1674 (earlier editions of both these works must have appeared), and to this Creighton made a reply, ultimately enhancing his reputation more in continental Europe than in Great Britain.