Joseph Addison Woodward (April 11, 1806 – August 3, 1885) was a U.S. Representative from South Carolina, son of William Woodward.
Born in Winnsboro, South Carolina, Woodward received an academic training and was graduated from the University of South Carolina at Columbia. He studied law. He was admitted to the bar and practiced. He served as member of the State house of representatives from 1834 to 1835 from 1840 to 1841.
Woodward was elected as a Democrat to the Twenty-eighth and to the four succeeding Congresses (March 4, 1843 – March 3, 1853). He declined to be a candidate for reelection in 1852 to the Thirty-third Congress.
After leaving Congress, he moved to Alabama and resumed the practice of law. He died in Talladega, Alabama, on August 3, 1885. He was interred in Oak Hill Cemetery.