Barzda was primarily a midget racing and sprint car racing driver but made ten starts in the USAC National Championship from 1952 to 1959. His best race finish was a pair of fourth places in 1958 at Springfield and Trenton. He finished 18th in the 1958 National Championship. He unsuccessfully attempted to qualify for the Indianapolis 500 in 1951, 1952, and 1953. He retired after he was involved in a crash at Williams Grove Speedway in 1959 where Van Johnson died. Barzda survived with minor injuries.
He and his brother Jim owned California Speed Shop in New Brunswick, New Jersey and continued to field racing cars after Joe's retirement from the cockpit.
- Van Johnson, veteran race driver, killed in Grove crash, The Gettysburg Times, July 20, 1959, Retrieved 2013-09-01
- Joe Barzda Entered In Opener, Reading Eagle, March 27, 1959, Retrieved 2013-09-03
- Joe Barzda, Old Racing Cars, Retrieved 2013-09-03