Sir Robert Monckton-Arundell, 4th Viscount Galway PC (4 July 1752 – 23 July 1810), was a British politician of the late 18th and early 19th centuries. He was a younger son of William Monckton-Arundell, 2nd Viscount Galway and succeeded his elder brother Henry to the title in 1774. He was elected Member of Parliament to represent Pontefract from 1780 to 1783, made a Privy Counsellor in 1784 and knighted in 1786. He was MP for York from 1783 to 1790 and again for Pontefract from 1796 to 1802.