Rhodes was born in Nashville, Tennessee and attended the city's public schools. He learned the game of golf in his teenage years while working as a caddie at Nashville's Belle Meade Country Club and Richland Country Club. In the late 1930s, Rhodes joined the Civilian Conservation Corps (CCC). He served in the United States Navy in World War II. When his tour of duty concluded, Rhodes was discharged in Chicago, where he met entertainer Billy Eckstine and heavyweight boxing champion Joe Louis. He taught both men to play the game of golf, and served as Louis' personal instructor, valet and playing partner.
In the late 1940s, Rhodes moved to southern California where he was mentored by Ray Mangrum. In 1948, he played in the U.S. Open at the Riviera Country Club in Los Angeles, California and became recognized as the first African-American professional golfer. Rhodes and fellow African-American golfer Bill Spiller initiated litigation against the Professional Golfers' Association of America (PGA) seeking removal of the association's "Caucasian only clause". Although they prevailed in the out-of-court settlement, the PGA circumvented the agreement by changing its tournaments to "invitationals" and invited only whites to participate.
Rhodes returned to his native Nashville in the 1960s and mentored several black PGA players including Lee Elder and Charlie Sifford. He died at the age of 55. A month after his death, the Cumberland Golf Course in Nashville was renamed in his honor. In 1998, Rhodes was inducted into the Tennessee Golf Hall of Fame.
- "Leaders of Afro-American Nashville". Retrieved 2008-01-31.
- Glenn, Rhonda (February 6, 2007). "Paving The Rhodes For Other African-American Golfers". United States Golf Association. Archived from the original on 2008-03-31. Retrieved 2008-01-31.
- PGA of America bestows membership upon late African-American pioneers