Team Logo. The San Antonio Thunder was a team in the North American Soccer League (1968-1984). They missed the playoffs in both of their seasons. In 1977 they moved and became Team Hawaii. Retrieved from "https://prosportsteams.fandom.com/wiki/San_Antonio_Thunder?oldid=16924" Categories: NASL (1968-1984) Teams Teams in Texas Teams in San Antonio Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.