Born in Bullitt County, Kentucky, Peyton completed preparatory studies. He was graduated from the medical department of Transylvania University, Lexington, Kentucky, in 1827 and began practice in Hartford, Kentucky. He served as member of the Kentucky House of Representatives in 1835.
Peyton was elected as a Democrat to the Thirtieth Congress (March 4, 1847 – March 3, 1849). He was an unsuccessful candidate for reelection in 1848 to the Thirty-first Congress.
Peyton was elected to the Thirty-fifth and Thirty-sixth Congresses (March 4, 1857 – March 3, 1861). He was an unsuccessful candidate for renomination in 1860. He resumed the practice of medicine. He died in Hartford, Kentucky, January 4, 1870. He was interred in Oakwood Cemetery.