Henry Torrens Anstruther (27 November 1860 – 5 April 1926) was a British Liberal Unionist politician.
The second son of Sir Robert Anstruther, 5th Baronet MP, he was educated at Eton and Edinburgh University. He became an advocate in Edinburgh in 1884, and was Liberal Unionist Member of Parliament for St Andrews Burghs from 1886–1903 in succession to his father. He served in government as a Lord of the Treasury from 1895–1903.
He was a Justice of the Peace for Buckinghamshire and Fife, and from 1903 was a member of the Administrative Council of the Suez Canal Company. He was an Alderman on London County Council from 1905–1910. He was father of the writer Joyce Anstruther, better-known via her pen-name of Jan Struther.