Robert Anstruther may refer to:

• Sir Robert Anstruther, 1st Baronet (1658–1737), (additionally of Balcaskie, Fife and Braemore, Caithness in 1698) MP for Fife 1710
• Robert Anstruther (British Army colonel), of the 58th (Rutlandshire) Regiment of Foot (renumbered in 1757 from 60th Regiment of Foot) 1755-68
• Sir Robert Anstruther, 3rd Baronet (1733–1818), of the Anstruther baronets
• Robert Anstruther (MP) (1757–1832), MP for Anstruther Burghs 1793 to 1794
• Robert Anstruther (British Army officer) (1768–1809), Scottish general
• Sir Robert Anstruther, 5th Baronet (1834–1886), MP for Fife 1864–1880 and St.Andrews 1885–1886, Lord Lieutenant of Fife 1864–1886
• Robert Hamilton Anstruther (1862–1938), Royal Navy officer

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