Currence pitched for Emmett Scott High School in Rock Hill and was signed as a free agent in 1970 by the Pittsburgh Pirates. In 1973, he was traded to the Milwaukee Brewers for Greg Erardi., and he pitched in the Class A Midwest League's 1974 All-Star Game, representing the Danville Warriors, a Brewers affiliate. Currence pitched at the Major League level with the Brewers in 1975 in eight games, making one start, wearing #20. He was called up from the Brewers' AA level Eastern League team, the Thetford Mines Miners in Thetford Mines, Quebec, Canada when pitcher Ed Sprague, Sr. was put on the 60-day disabled list in July 1975. Currance started the next season with the Spokane Indians, the Brewers' AAA farm club in the Pacific Coast League, and split time that season between Spokane and the Berkshire Brewers, the new Brewers' AA Eastern League farm team. His career in organized baseball ended with 4 games at the AA level in the Eastern League with the Holyoke Millers (the third Brewers affiliated AA Eastern League location in three years) in 1977. Currence was named to the York County (South Carolina) Sports Hall of Fame in 2011.