Sir Robert Sutton CB PC (1671 – 13 August 1746) was an English diplomat and later a politician.
He was the elder son of Robert Sutton of Averham, Nottinghamshire, and his wife, Katherine, the daughter of the Revd William Sherborne of Pembridge, Herefordshire. He was admitted to Trinity College, Oxford in 1688 and went on the Middle Temple in 1691.
He was ordained a deacon and became chaplain to his cousin Robert Sutton, 2nd Baron Lexinton, English Envoy in Vienna in 1694. In 1697, he was appointed as secretary to the British legation there, and upon the departure of bis cousin became the English resident there. Lexinton then secured for him the nomination for English ambassador to the Ottoman Empire in Constantinople on 5 December 1700, and he arrived in Adrianople on 7 January 1702.
He asked to be recalled on 6 May 1715. He remained there until summer 1717, when he travelled to Vienna, arriving on 17 September. Afterwards he served with Abraham Stanyan as joint mediator at the Austro-Turkish peace congress at Passarowitz in 1718. His final diplomatic posting was as ambassador to France in 1720, but was superseded the following year. Following his return to England, he bought estates in Lincolnshire and Nottinghamshire, worth nearly £5000 a year, with a house at Broughton, Lincolnshire.