Nelson attended Arizona State University and was selected by Seattle in the 1981 MLB draft. He made his MLB debut on May 17, 1983, against the California Angels. His most productive MLB season came in 1983, when he registered 291 at-bats in 98 games, recording a .254 batting average. He made his final MLB appearance on August 2, 1986, at the Kingdome, appearing as a pinch runner in a 7-3 Seattle victory over the California Angels.