Richard C. Byrd was born in 1805 in Hawkins County, Tennessee. Byrd was a merchant and farmer. He moved to Arkansas in 1826.
Byrd became auditor for the Arkansas Territory and served in that position from 1829 to 1831. He served in the Territorial Legislature in 1833. He became a member of the Arkansas House of Representatives in 1836 and served in the Arkansas Senate in 1840, 1842, 1846, and 1848. Byrd had an unsuccessful gubernatorial run in 1844.
Governor Thomas Stevenson Drew resigned from office. Byrd was president of the Senate and became acting governor. Byrd left the office on 19 April 1849 and returned to his store in Jefferson County, Arkansas.