Born in Alexandria, Virginia, on September 9, 1812 Stanton completed preparatory studies, attended Alexandria Academy, studied law and was admitted to the bar, commencing practice in Maysville, Kentucky in 1835. He was editor of the Maysville Monitor from 1835 to 1842 and served as postmaster of Maysville. He was elected a Democrat to the United States House of Representatives in 1848, serving from 1849 to 1855. There, he served as chairman of the Committee on Public Buildings and Grounds from 1849 to 1853 and of the Committee on Elections from 1853 to 1855. He was unsuccessful for reelection in 1854. Afterwards, Stanton served as a state's attorney from 1858 to 1861, was a delegate to the Democratic National Convention in 1868 and was a district judge from 1868 to 1874. He resumed practicing law until his retirement in 1885 and died on March 20, 1891 in Maysville, Kentucky. He was interred there in Maysville Cemetery.
Stanton is credited with naming Washington Territory, later the state of Washington, during an 1853 debate over the territory's preferred name of "Columbia".