On June 10, 2000, Giguère was traded to the Mighty Ducks of Anaheim in exchange for a second-round pick in 2000 (later traded to the Washington Capitals; the Capitals selected Matt Pettinger). He began the 2000-01 season with the Mighty Ducks' farm team, the Cincinnati Mighty Ducks, until he was recalled from the AHL. Giguère eventually took over Dominic Roussel's backup position to starter Guy Hebert. Due to only brief stints in the NHL during his tenures with Hartford and Calgary, the 2000–01 season qualified as Giguère's rookie NHL season. He played in 34 games, posting a 2.57 GAA and .911 save percentage.