Moore was initially projected to be a top ten draft pick at the end of the 2012 season. One of his strengths was his versatility while playing in Texas A&M. Where he played as 3-4 outside linebacker in his first two seasons and tallied a total of 14 sacks in that time span. In 2012 as the starting defensive end he exploded with 12.5 sacks. Despite his previous accomplishments, his status as a top ten pick was damaged because of his poor performance at the NFL Combine, where he had only 12 reps in the bench press (lowest among defensive linemen) and a 4.95 time in the 40-yard dash. He was projected by many draft analysts to go in the late first or early second round; however, he slid down the draft board and was eventually chosen by the New York Giants in the third round, with the 81st overall pick.
Though some teams viewed Moore as a 3–4 outside linebacker, the Giants selected him as a 4–3 defensive end. He saw action in 15 games during the regular season, during which time he recorded 11 tackles and 1 forced fumble. The latter occurred during a Monday Night Football game against the Vikings when Moore stripped the ball while playing kickoff coverage.
Moore recorded his first career sack during his second season on September 25, 2014 against the Washington Redskins.
On December 11, 2015, Moore was waived for violating team rules, reportedly due to having an altercation with fellow defensive lineman Cullen Jenkins regarding headphones. The incident with Jenkins was one of several altercations Moore had with teammates during the 2015 season, according to Jay Glazer of Fox Sports.
On November 1, 2016, Moore was signed by the Seattle Seahawks. He was placed on the injured reserve list on December 20, after suffering a foot injury. He made 7 tackles and half a sack, while playing in 4 games. The injury forced him to miss 3 of his last 4 contests.
On March 10, 2017, Moore was signed as a free agent by the Dallas Cowboys to play defensive end. He was suspended for the first two games of the regular season for violating the NFL's substance abuse policy, which was a situation the Cowboys were aware of before he was signed. On October 24, he was released to create space to sign Mike Nugent following the groin injury to placekickerDan Bailey. He was a backup player, registering 7 tackles, 4 quarterback hurries in 3 games and was declared inactive in one contest.
On January 10, 2019, Moore signed with the San Diego Fleet of the Alliance of American Football. He played with the team until the league folded in April. He was considered one of the top defensive players in the league, registering 22 tackles, 7 sacks and one fumble recovery.