Adam Rankin Alexander was an American politician that represented Tennessee in the United States House of Representatives. He was born in Rockbridge County, Virginia on November 1, 1781. He became a member of the Tennessee Senate in 1817. Prior to being a state senator, he worked as a surveyor, and afterwards, he was the register of the land office for the tenth surveyors' district in Madison County, Tennessee. He was a member of the court of Madison County in 1821.
Adam Alexander was elected as a Jacksonian Republican to the Eighteenth and as a Jacksonian to the succeeding Congress. He served as a U.S. Representative from March 4, 1823 to March 3, 1827. He was an unsuccessful candidate for re-election to the Twentieth Congress in 1828.
Adam Alexander represented Shelby County, Tennessee at the Tennessee constitutional convention in 1834. He was a member of the Tennessee House of Representatives in 1841 and 1843. He died on November 1, 1848 in Marshall County, Mississippi. He was interred in Pryor Cemetery in Marshall County, Mississippi.