An 1827 graduate of the university, Alexander was a lawyer and judge. In 1838 he was appointed attorney general for the second circuit and served until fall 1838. In 1844 he was appointed circuit court judge and served until his death, having been once appointed by the legislature and once elected by the people. He was a trustee of East Tennessee Female Academy and continued to serve as a trustee for its successor, the East Tennessee Female Institute. He was a trustee of Old Gray Cemetery from 1852 to 1855.