Colonel Robert Anstruther (31 December 1757 – 1832) was a Scottish soldier in the British Army, and briefly a politician.
He was the son of Sir John Anstruther of that Ilk, 2nd Bt. and Janet Fall. He married Anne Nairne, daughter of Colonel Alexander Nairne and Preston née Balneavis on 9 May 1801.
He was the Member of Parliament (MP) for Anstruther Burghs from 1793 to 1794. He gained the rank of Colonel in the service of the 68th Regiment.