Rivet was drafted by the Montreal Canadiens in the 1992 NHL Entry Draft from the Kingston Frontenacs in the Ontario Hockey League. He was drafted in the third round, 68th overall. Upon being drafted, he recorded junior career highs in 1992–93 with 19 goals, 55 assists, and 74 points. He added 12 points in the playoffs as Kingston advanced to the semi-finals but were eliminated by the Peterborough Petes in five games.