On January 12, 2012, it was announced that Norman had accepted his invitation to play in the East-West Shrine Game. Norman was projected to be a late round pick at the end of his senior season, but began to climb draft boards after impressing scouts during East-West Shrine Game practices. On January 21, 2012, Norman played in the 2012 East-West Shrine Game and was part of the East team that lost 24-17 to the West. On January 26, 2012, Norman accepted an invitation to play in the 2012 Senior Bowl as a late-replacement after Alfonzo Dennard sustained an injury. Norman continued to impress coaches and scouts by intercepting six passes during Senior Bowl practices, although he was a late-replacement and had minimal time to practice with his team. On January 28, 2012, he played in the 2012 Senior Bowl as part of Minnesota Vikings’ head coach Leslie Frazier's North team that defeated the South 23-13.
He attended the NFL Scouting Combine in Indianapolis and completed all of the combine drills. His mediocre performance in the 40-yard dash (4.66s) possibly resulted in a fall in his draft stock. On March 27, 2012, Norman participated at Coastal Carolina's pro day and chose to perform combine and positional drills. He improved his time in the 40-yard dash (4.57s), 20-yard dash (2.63s), and three-cone drill (6.92s). Norman attended a pre-draft visit with the Detroit Lions. It was reported that team representatives and scouts from 27 NFL teams attended Coastal Carolina's pro day. At the conclusion of the pre-draft process, Norman's draft projections varied from as early as the third round to as late as the seventh round by NFL draft experts and scouts. The majority of NFL draft experts projected Norman to be a third or fourth round pick. He was ranked the eighth best cornerback prospect in the draft by NFL analyst Mike Mayock, 10th best by Scouts Inc., 28th best CBS Sports, and 29th best by DraftScout.com.
The Carolina Panthers selected Norman in the fifth round, 143rd overall, of the 2012 NFL Draft. Norman was the 14th cornerback drafted in 2012 and became only the third player to be drafted from Coastal Carolina, after Tyler Thigpen (2007) and Jerome Simpson (2008).
On May 10, 2012, Norman signed his four-year rookie contract with the Panthers, worth US$2.3 million. Throughout training camp, Norman competed to be a starting cornerback against Captain Munnerlyn and Brandon Hogan. Head coach Ron Rivera named Norman and Chris Gamble the starting cornerbacks to begin the regular season.
He made his professional regular season debut and first career start in the Panthers' at the Tampa Bay Buccaneers and recorded four combined tackles during their 16–10 loss. In Week 3, he collected a season-high 11 combined tackles (eight solo) and a pass deflection during a 36–7 loss to the New York Giants. Norman became a focal point of the secondary after the Carolina Panthers placed Chris Gamble on injured reserve due to a shoulder injury on October 22, 2012. On October 28, 2012, Norman recorded five combined tackles, deflected a pass, and made his first career interception in the Panthers’ 23-22 loss at the Chicago Bears in Week 8. Norman intercepted a pass by Bears’ quarterback Jay Cutler, that was originally intended for wide receiver Brandon Marshall, during the first quarter. Norman began to struggle towards the end of his rookie season and was eventually surpassed on the depth chart by Josh Thomas and was relegated to a backup cornerback beginning in Week 14. In Week 15, Norman was surpassed on the depth chart by James Dockery and became the fourth cornerback on the depth chart. He finished his rookie season in 2012 with 73 combined tackles (52 solo), seven pass deflections, and one interception in 16 games and 12 starts.