Peca was selected by the Tampa Bay Lightning in the seventh round (No. 201) of the 2011 NHL Draft. He played four seasons with Quinnipiac University (2011-15) where he finished sixth in career scoring with 143 points (42 goals, 101 assists) in 157 games and led them to the 2013 NCAA championship game.

On April 1, 2015, Peca signed a two-year, two-way contract with the Lightning.

The following season, he had 43 points (eight goals, 35 assists) in 65 games with Syracuse of the American Hockey League. In 2016-17, he had 41 points (12 goals, 29 assists) in 68 games with Syracuse and was recalled by Tampa Bay on Dec. 27, 2016. He made his NHL debut the next night against the Montreal Canadiens and scored his first career goal on Jan. 3, 2017 in a 6-4 loss to the Winnipeg Jets. Peca, who finished the season with two points (one goal, one assist) in 10 games, became the first player from Quinnipiac to score a goal in the NHL.

On July 5, 2017, the Lightning re-signed Peca to a one-year, two-way contract.

He spent most of the 2017-18 season with Syracuse, where he had 46 points (13 goals, 33 assists) in 63 games, but was recalled by the Lightning on Jan. 21, 2018 and had five points (two goals, three assists) in 10 games.

He signed with the Montreal Canadiens as a free agent July 1, 2018. He split the 2018-19 season with Laval of the AHL and the Canadiens, scoring 10 points (three goals, seven assists) in 39 games with Montreal.

Peca was traded to the Senators on Feb. 24, 2020.