Carter attended and played college football at Georgia under head coaches Mark Richt and Kirby Smart. As a true freshman at Georgia, Carter played 13 games making 5 starts, and received the University of Georgia newcomer of the year award. After the 2016 season, Carter announced that he would return to school for his senior season, despite speculation that he might declare for the 2017 NFL draft.
Carter attended the NFL Scouting Combine and completed the majority of drills, but opted to skip the bench press, short shuttle, and three-cone drill. Carter was a top performer among all of the edge rushers, finishing first in the broad jump, second in the 40-yard dash, and third among his position group in the vertical jump. On March 21, 2018, Carter participated at Georgia's pro day, but opted to stand on his combine numbers and only performed positional drills. He attended pre-draft visits and private workouts with the San Francisco 49ers, Denver Broncos, and Minnesota Vikings. At the conclusion of the pre-draft process, Carter was projected to be a second round pick by NFL draft experts and scouts. He was ranked as the second best outside linebacker by DraftScout.com and was ranked the fifth best defensive end by Scouts Inc.
On May 10, 2018, the New York Giants signed Carter to a four-year, $4.08 million contract that includes a signing bonus of $1.04 million. In Week 3, against the Houston Texans, Carter recorded his first professional sack.