Born in Baraboo, Wisconsin, Barnes was in the United States Navy Reserve from 1918 to 1921. He received a Bachelor's Degree of Arts from UC Berkeley in 1922 and a J.D. from University of California, Berkeley, Boalt Hall School of Law in 1925. Barnes also studied at Harvard Law School. He was in private practice in San Francisco, California from 1925 to 1928, and then in Los Angeles, California until 1947. He was a lecturer at the University of Southern California Law School and Medical School from 1947 to 1952. He was a presiding judge of the Superior Court of the State of California for the County of Los Angeles from 1947 to 1953. He was an Assistant U.S. Attorney General in Washington, D.C. from 1953 to 1956.
On March 5, 1956, Barnes was nominated by President Dwight D. Eisenhower to a seat on the United States Court of Appeals for the Ninth Circuit vacated by William Edwin Orr. Barnes was confirmed by the United States Senate on March 20, 1956, and received his commission on March 21, 1956. He assumed senior status on October 31, 1970, serving in that capacity until his death.