Maciver finished the 1995-96 with the Winnipeg Jets. He played in his first game with the Jets on December 28, 1995, scoring an assist in a 4–3 loss to the Chicago Blackhawks. On January 5, 1996, Maciver scored his first goal as a member of the Jets, scoring against Darcy Wakaluk of the Dallas Stars in a 5–4 loss. In 37 games played with the Jets, Maciver scored five goals and 30 points, helping the club reach the post-season. On April 17, 1996, Maciver played in his first playoff game with Winnipeg, earning no points in a 4–1 loss to the Detroit Red Wings. On April 28, 1996, Maciver scored his first playoff goal with the Jets, scoring against Mike Vernon of the Red Wings in a 4–1 loss. The loss eliminated the Jets from the post-season, and Maciver scored the last goal in Winnipeg Jets history, as the club relocated to Phoenix, Arizona during the off-season.