Norris appeared in 20 National Hockey League regular season games for the Nordiques and the Mighty Ducks of Anaheim, scoring 2 goals and 4 assists for 6 points and collecting 8 penalty minutes.

In 2002, he won the German Championship with Köln when they beat perennial rivals Adler Mannheim 3–2 in the best-of-five final series with Norris netting the game winner in each of Colognes victories.

In 2007 Norris retired from active play and, in a surprise move by his last club, was hired as the Lions' general manager in 2007, a position he held until the team filed for bankruptcy in May 2010[citation needed].

[4][5] Son Josh Norris was a first-round selection of the San Jose Sharks in the 2017 NHL Entry Draft[6] and is currently a player for the Ottawa Senators.

His younger brother Warren Norris played professionally with the St. John's Maple Leafs and Grand Rapids Griffins.