Parker joined UCLA in 2012 as part of the top recruiting class in the nation, and helped the school to three NCAA tournaments, including consecutive Sweet 16 appearances in 2014 and 2015.

[1] Growing up, Parker would tag along with his older brother, Adrian, and watch him play basketball at a local court.

[2] By the seventh grade, Parker stood 6 feet 3 inches (1.91 m) and weighed 300 pounds (140 kg), and would be mistaken for a lineman.

[4] He was named Mr. Georgia Basketball as the top player in the state, and was recognized nationally as a Parade, McDonald's and Jordan Brand All-American.

[1] Parker chose to play college basketball at UCLA over Kansas, Duke, Ohio State, Memphis, and Georgia.

[4][8] Parker joined Shabazz Muhammad, Kyle Anderson and Jordan Adams in a UCLA recruiting class considered the best in the nation.

[9] Bothered by injuries and lack of conditioning, the 6-foot-9-inch (2.06 m), 275-pound (125 kg) Parker did not play much as a freshman in 2012–13, averaging 2.4 points and 1.4 rebounds in 6.3 minutes per game.

However, Coach Ben Howland rarely played Parker off the bench, relying instead on 6-foot-10-inch (2.08 m) twins David and Travis Wear, who were primarily jump shooters as opposed to post players.

[17] He was the final player remaining from the highly touted 2012 recruiting class—the other three had moved on to the National Basketball Association (NBA).

He returned against Utah, when the Bruins earned their best win of the season as Parker's inside play balanced their offense that had become overly dependent on their perimeter players.

[21] On March 21, 2015, in the 2015 NCAA tournament, Parker scored a career-high 28 points and added 12 rebounds in a 92–75 win over UAB, helping the Bruins advance to the Sweet 16 for the second straight year.

[22] Parker returned as the Bruins' lone senior in 2015–16,[17] but the team did not advance to the NCAA Tournament for the first time in his career.

[1] With Kevon Looney having left for the NBA, Parker was moved to forward and Thomas Welsh entered the starting lineup at center.

[23][24] Parker was named to the initial watch list of twenty candidates for the Karl Malone Award, given annually to the top power forward in Division I men's basketball.