In the 1981 NFL Draft, Taylor was drafted by the NFL's New York Giants in the first round as the 2nd pick overall. In a poll of NFL General Managers (GMs) taken before the draft 26 of the league's 28 GMs said if they had the first selection they would select Taylor. One of the two GMs who said they would not take Taylor was Bum Phillips, who had just been hired as coach and general manager by the New Orleans Saints. As fate would have it for Taylor, the Saints were also the team who had the first pick in the draft. Giants GM George Young predicted before the draft that he would be better than NFL legends such as Dick Butkus: "Taylor is the best college linebacker I've ever seen. Sure, I saw Dick Butkus play. There's no doubt in my mind about Taylor. He's bigger and stronger than Butkus was. On the blitz, he's devastating."
Taylor's talent was evident from the start of training camp. Reports came out of the Giants training compound of the exploits of the new phenom. Taylor's teammates took to calling him Superman and joked that his locker should be replaced with a phone booth. Phil Simms, the team's quarterback, said, "on the pass rush, he's an animal. He's either going to run around you or over you. With his quickness, he's full speed after two steps." Taylor made his NFL exhibition debut on August 8, 1981, recording 2 sacks in the Giants' 23–7 win over the Chicago Bears. Before the season word spread around the league about Taylor. Years after facing him in an exhibition game, Pittsburgh Steelers Quarterback Terry Bradshaw recalled, "[h]e dang-near killed me, I just kept saying, 'Who is this guy?' He kept coming from my blind side and just ripped my ribs to pieces."
Taylor made his NFL regular season debut on September 6, 1981, in a 24–10 loss to the Philadelphia Eagles. Aside from incurring a penalty for a late hit on Eagles running back Perry Harrington, Taylor played a nondescript game. In a game versus the St. Louis Cardinals later in the season, Taylor rushed and sacked the passer when he was supposed to drop into coverage. When told by Parcells that was not what he was assigned to do on that play, and that what he did was not in the playbook, Taylor responded "Well, we better put it in on Monday, because that play's a dandy." He recorded 9.5 sacks in 1981, and his rookie season is considered one of the best in NFL history. He was named 1981's NFL Defensive Rookie of the Year and Defensive Player of the Year, making him as of 2020 the only rookie to win an Offensive or Defensive Player of the Year award. Taylor's arrival helped the Giants defense reduce their points allowed from 425 points in 1980 to 257 in 1981. They finished the season 9–7, up five games from the previous season, and advanced to the NFL divisional playoffs, where they lost 38–24 to the eventual Super Bowl champion San Francisco 49ers. The San Francisco win was due partly to a new tactic 49ers coach Bill Walsh used to slow Taylor. Walsh assigned guard John Ayers, the team's best blocker, to block Taylor and, although Taylor still recorded a sack and three tackles, he was not as effective as normal. In contrast to his on-field success Taylor was already developing a reputation for recklessness off the field; after nearly getting killed during the season when his speeding resulted in a car crash, Young told the team's trainer he would be surprised if the linebacker lived past the age of 30, and the Giants insured Taylor's life for $2 million.