Sir Robert Anstruther, 1st Baronet (24 September 1658 – March 1737) was a Scottish politician.
He was made a baronet in 1694, Wrae, Linlithgowshire, and Balcaskie, Fife and Braemore, Caithness.
Anstruther was Member of Parliament for Fife from 24 March 1709 to 24 October 1710.