Born near Littleton, North Carolina in Halifax County, Alston was said to have attended Princeton College, though no records exist of his enrollment. He then engaged in agricultural pursuits. He was elected to the North Carolina House of Commons in 1790 and served for two years; in 1794 he was elected to a single term in the North Carolina Senate.
In 1798, Alston was elected as a Federalist to the U.S. House, defeating incumbent Thomas Blount and two other candidates. Alston served from March 4, 1799 to March 3, 1815. Early in the Jefferson administration, Alston changed parties and became affiliated with the Republican Party. Local Federalists recruited former Gov. William R. Davie to challenge Alston in 1803, but Alston survived Davie's challenge. Alston chaired the House Committee on Revisal and Unfinished Business during the 13th U.S. Congress. In the election of April 1813, Alston defeated Daniel Mason, the Peace candidate, with the smallest margin of his re-election campaigns (56%-44%), and Alston retired at the end of the term.
He returned to the state House of Commons between 1820 and 1824, and then returned to Washington in 1825, elected as a Jacksonian Democrat. Serving three terms (March 4, 1825 – March 3, 1831), Alston chaired the Committee on Elections during the 21st Congress. He declined to seek re-election in 1830 and returned to agriculture. Alston died in 1837 in Halifax and is buried at his plantation home of Butterwood, near Littleton.
Alston's granddaughter, Missouri Alston Pleasants, established the Alston-Pleasants scholarship fund in his memory.