Richard Franklin Simpson (March 24, 1798 – October 28, 1882) was a U.S. Representative from South Carolina. Born in Laurens, South Carolina, Simpson graduated from South Carolina College (now the University of South Carolina) at Columbia in 1816. He studied law and was admitted to the bar in 1819. He began practice in Pendleton, South Carolina. He held several local offices. He served as major during the Second Seminole War in 1835. He volunteered with the Laurens County Company and was elected Captain of the Company. He was appointed Major of the South Carolina Regiment, and took his cavalry Battalion to Florida.