After three seasons with Penticton of the British Columbia Hockey League, where he was named the 2012-13 BCHL Interior Conference Defenseman of the Year, Stecher played at the University of North Dakota. In three seasons, he scored 53 points (13 goals, 40 assists) in 119 games before he was signed as a free agent to a two-year, entry-level contract with the Vancouver Canucks on April 13, 2016.

As a junior in 2015-16, Stecher scored 29 points (eight goals, 21 assists) and was plus-26, helping North Dakota win the NCAA championship. He was named to the All-America West Second Team by the America Hockey Coaches Association.

Stecher began his first professional season with Utica of the American Hockey League, playing four games before being called up by the Canucks on Oct. 24, 2016. He made his NHL debut the following night against the Ottawa Senators and scored his first goal in a 5-4 overtime win against the Dallas Stars on Nov. 13, 2016. Stecher finished the season with 24 points (three goals, 21 assists) in 71 games.

He played 68 games for Vancouver in 2017-18 and scored 11 points (one goal, 10 assists), missing 14 games because of a knee injury.

Stecher played for the Detroit Red Wings, Los Angeles Kings and Arizona Coyotes in subsequent seasons. He was traded to the Calgary Flames by Arizona with Nick Ritchie for Brett Ritchie and Connor Mackey on March 3, 2023. He re-signed with the Coyotes on July 1, 2023, and was traded to the Edmonton Oilers on March 7, 2024, for a fourth-round pick in the 2027 NHL Draft.

Stecher signed a two-year, $1.575 million contract to stay with the Oilers on July 1, 2024.