Sir Robert Clayton, 3rd Baronet ( – 10 May 1799) was an English politician.
He was the only son of Sir Kenrick Clayton, 2nd Baronet of Marden Park, Surrey, whom he succeeded in 1769.
He was a Member of Parliament (MP) for Bletchingley from 1768 to 1783, for Surrey from 1783 to 1784, for Bletchingley again from 1787 to 1796, and for Ilchester from 1796 until his death.
He died in May 1799. He had married Mary, the daughter of Frederick Standert of Greenwich but left no children. The baronetcy was therefore inherited by his first cousin, Sir William Clayton, 4th Baronet, the son of his father's younger brother William.