Soucy was a fifth-round pick (No. 137) of the Minnesota Wild in the 2013 NHL Draft. He played four seasons for the University of Minnesota Duluth before signing a two-year contract with the Wild on April 11, 2017 and reporting to Iowa of the American Hockey League.
Soucy, a defenseman, had 15 points (three goals, 12 assists) in 35 games of his senior season to help UMD reach the NCAA championship game, a 3-2 loss to the University of Denver. He had 47 points (12 goals, 35 assists) in 174 collegiate games. He spent most of the 2017-18 season with Iowa of the American Hockey League, finishing with 15 points (one goal, 14 assists), but made his NHL debut with the Wild on April 2, 2018, and was scoreless in three games. He also dressed for four games during Minnesota's loss to the Winnipeg Jets in the Western Conference First Round of the Stanley Cup Playoffs.