2009-10: Cody Corbett played for the junior varsity team at Minnesota's Stillwater High School as a tenth grader.
2010-11: Corbett skated for Metro Northeast in the Upper Midwest Elite High School League in the fall before taking the ice for Stillwater High School as a junior. He scored 1 goal with 2 assists in five games for Metro Northeast. During the high school season Corbett scored 9 goals with 13 assists and 14 penalty minutes in 26 games. Stillwater finished second to White Bear Lake in the Suburban East Conference and reached the Section 4AA semifinals.
2011-12: Corbett began the year playing in the Upper Midwest Elite High School League before joining the WHL's Edmonton Oil Kings at the end of October rather than playing his senior season at Stillwater. Playing for the WHL champions, Corbett scored 6 goals with 20 assists and was +36 with 24 penalty minutes in 54 regular season games. He had 4 assists and was +2 with 14 penalty minutes in 18 WHL playoff games. Corbett played in two games at the Memorial Cup; finishing -4 with no points nor penalties. He was ranked 117th amongst North American skaters in Central Scouting's final rankings but was not selected in the 2012 NHL Draft.
2012-13: Corbett attended the Minnesota Wild's prospect camp in July and returned to Edmonton for his second season with the Oil Kings. He was the team's top scoring defenseman with 7 goals and 35 assists and finished +38 with 48 penalty minutes in 71 regular season games. The Oil Kings finished first in the Central Division and reached the WHL Finals against Memorial Cup-bound Portland. Corbett scored 2 goals with 8 assists and was +9 with 14 penalty minutes in 20 playoff games.
2013-14: Corbett skated for Minnesota in the 2013 Traverse City Prospect Tournament and attended camp with the Wild but did not sign a contract before returning to Edmonton. He was an assistant captain in his third season with the Oil Kings and again led Edmonton's defensemen in scoring. He scored 17 goals with 44 assists (both career highs) and was +19 with 37 penalty minutes in 65 regular season games. The Oil Kings and Calgary each finished with 103 points; with the Hitmen finishing first in the Central Division based on more wins. Corbett signed a three-year, entry-level contract with Colorado as a free agent on March 5th, 2014.
Colorado signed Corbett to a three-year entry-level contract on March 5th, 2014.