In 1990, Quinn was traded to the Vancouver Canucks in 1990; that started a period where Quinn played for seven teams in five years. In 1992, Quinn was alleged to have raped a 19-year-old woman in a hotel room. He was released by the Minnesota North Stars, the team he was playing for at the time. Quinn maintained that he and the woman had sex, but that it was consensual. The police did not press charges, and Quinn was back in the NHL the next season.