Moore attended Deer Valley High School, where he played as a wide receiver and defensive back. He also practiced basketball. He moved on to Laney College, where he became a starter at cornerback, appearing in 10 games as a freshman, while making 30 tackles, five interceptions, 9 passes defensed and one forced fumble. The next year, he received All-JUCO honors. After his sophomore season, he transferred to Southern Methodist University. He finished his college career after appearing in 19 games, while posting 59 tackles, 2 interceptions, 18 passes defensed, 2 sacks and one fumble recovery.
On July 28, 2011, he was signed by the Oakland Raiders as an undrafted free agent. He was waived on September 3 and re-signed the next day to the practice squad. He was released on September 26.
On October 5, 2011, he was signed by the New England Patriots to their practice squad. On October 15, he was signed to the active roster and made his NFL debut against the New York Jets on November 13, starting every snap at safety for the Patriots. On December 10, 2011, Moore was released by New England. On December 14, 2011, he was re-signed to the Patriots practice squad and on December 23, 2011, he was promoted to the active roster. On January 1, 2012, in Week 17 of the 2011-12 NFL season, Moore recorded two interceptions against the Buffalo Bills, returning one for a touchdown. Late in the AFC Championship against the Baltimore Ravens, he hit Lee Evans' arm, preventing a potential touchdown. Had Moore not made the play, Evans probably would have caught the ball and sent the Ravens to the Super Bowl. After the incomplete pass, Billy Cundiff missed a game-tying field goal as the Patriots went on to win 23-20, giving him an AFC Championship ring. On October 31, 2012, he was waived and re-signed to the Patriots practice squad two days later.
On November 30, 2012, he was signed by the Dallas Cowboys from the New England Patriots practice squad to replace an injured Orlando Scandrick. He played in the last five games of the season mostly in passing situations. Moore was released on August 31, 2013, in favor of rookie fourth round draft choice B.W. Webb. The team brought him back on November 25, to play as the fourth corner in passing situations. In 2014, after being mostly relegated to a reserve role during his career, he was named the team's nickel back during Orlando Scandrick's suspension and kept the role after Morris Claiborne suffered a season ending knee injury. He played in 16 games, registered 49 tackles and led all Cowboys defensive backs with 14 passes defensed.
On March 19, 2015, Moore signed with the Tampa Bay Buccaneers. He was used as the nickel cornerback in the first four games of the season, before being passed on the depth chart by Alterraun Verner and moved to a backup role. He was named the starting left cornerback in the seventh game of the season and had eight starts, before coming from the bench in the season finale. He registered 45 tackles, one interception, 6 passes defended, and 3 forced fumbles.
Buffalo Bills
Moore signed with the Buffalo Bills on April 5, 2016. On September 2, he was released as part of final roster cuts.
On September 6, 2016, Moore was signed by the New Orleans Saints to replace the recently released Cortland Finnegan. He played in 13 games with 12 starts for the Saints, recording career-highs with 56 tackles, 13 passes defensed along with two interceptions. On March 23, 2017, Moore re-signed with the Saints. With the emergence of their younger cornerbacks, the Saints released Moore on October 25, 2017. He was re-signed on November 20, 2017. He was released again on December 14, 2017. He was re-signed on December 21, 2017.
