Randall L. Gibson (September 10, 1832 - December 15, 1892) was a U.S. Senator and a member of the House of Representatives from Louisiana.
He was also an officer in the Confederate States of America military, a regent of the Smithsonian Institution, and a president of the board of administrators of Tulane University.
Gibson was the son of a plantation owner. He was a representative from 1875 to 1883 and a senator from 1883 to 1892. He was a Democrat. He died while still a senator in Hot Springs, Arkansas.