The team also waived rookie linebacker Brandon Marshall, a fifth-round draft pick, and veteran offensive lineman Herb Taylor on Saturday.
Adding Wilson could mean the Jaguars are uncertain about the status of starter Blaine Gabbert for Sunday's game at Green Bay. Gabbert is probable with an injured non-throwing shoulder. Chad Henne had been the team's only backup quarterback.
Wilson had been on the practice squad all season.
Chick has been sidelined since injuring his knee last season. He started practicing last week and could provide a much-needed boost to a defense that has an NFL-low five sacks.