2010-11: Anthony DeLuca led the Saint-Eustache Vikings in points and penalty minutes in his first season in Quebec midget AAA hockey and played for Team Quebec's U16 team in the Canada Winter Games. He scored 27 goals with 26 assists and had 78 penalty minutes in 39 regular season games. The Vikings finished second to Laval in the CCM Division. DeLuca scored 4 goals with 4 assists and 20 penalty minutes in nine playoff games as Saint-Eustache reached the semifinals. DeLuca scored 4 goals with 6 assists and had 10 penalty minutes in six games at the CWG as Team Quebec captured a silver medal. DeLuca was selected by Cedar Rapids in the fourth round (47th overall) of the 2011 USHL Futures Draft.
2011-12: DeLuca played for the Lac St-Louis Lions — leading Quebec midget AAA hockey with 80 points in his second season — and skated for Canada Quebec in the 2012 U17 World Hockey Challenge. He scored 48 goals with 32 assists and 68 penalty minutes in 43 games as Lac St-Louis finished second in the Reebok Division. DeLuca scored 3 goals with 3 assists and had 18 penalty minutes in four playoff games. He scored 3 goals in five games at the WHC. DeLuca was selected by Rimouski in the second round (22nd overall) of the 2012 QMJHL Entry Draft.
2012-13: DeLuca was the sixth-leading scorer on a veteran Rimouski team in his first QMJHL season. He scored 22 goals with 18 assists and was -7 with 33 penalty minutes in 67 games as the Oceanic finished second to Baie-Comeau in the East Division. DeLuca scored 1 goal and was -5 with 8 penalty minutes in the six-game first round playoff series with Gatineau.
2013-14: DeLuca had a breakout season in his second year with Rimouski. He led the Oceanic in scoring during the regular season with 35 goals and 43 assists and was +23 with 60 penalty minutes in 67 games. DeLuca was ranked 196th amongst North American skaters in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.