Robert Murray Gibson (August 20, 1869 – December 19, 1949) was a United States federal judge.
Born in Duncansville, Pennsylvania, Gibson received an A.B. from Washington and Jefferson College in 1889 and read law to enter the bar in 1894. He was an Assistant United States Attorney for the Western District of Pennsylvania from 1904 to 1914 and a special assistant to the U.S. Attorney General from 1912 to 1913. He was an assistant district attorney of Allegheny County, Pennsylvania from 1914 to 1922.
On July 18, 1922, Gibson was nominated by President Warren G. Harding to a seat on the United States District Court for the Western District of Pennsylvania vacated by Charles P. Orr. Gibson was confirmed by the United States Senate on July 24, 1922, and received his commission the same day. He served as chief judge from 1948 to 1949, assuming senior status on January 31, 1949. Gibson served in that capacity for less than a year, until his death, on December 19, 1949.