Anthony Martin Branch (July 16, 1823 – October 3, 1867) was a Texas politician who served in the Confederate States Congress during the American Civil War.
Branch was born in Buckingham County, Virginia, and later moved to Texas. He was a member of the Texas House of Representatives in 1859 and the Texas Senate in 1861.
During much of the Civil War, Branch served in the Confederate States Army as a captain in Company A, the 21st Texas Cavalry (also known as the 1st Texas Lancers.) He later represented Texas in the Second Confederate Congress in 1864 and 1865 until the end of the war.