Team Logo. The Tampa White Sox were a team in the Florida State League. They were the High-A affiliate of the Chicago White Sox. In 1989 they moved and became the Sarasota White Sox. Retrieved from "https://prosportsteams.fandom.com/wiki/Tampa_White_Sox?oldid=8497" Categories: Former FSL Teams Teams in Florida Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.