He made his MLB debut in 2012 for the Athletics before making his sole All-Star appearance two seasons later. The Athletics traded Norris to the San Diego Padres at the end of the season. He spent two seasons with the Padres, reaching career high statistics in runs, RBI, and home runs in 2015. The Nationals acquired Norris at the end of the 2016 season. Norris was granted free agency by the Nationals with the Tampa Bay Rays signing him. He was designated for assignment midway through the 2017 season, and after being released, he was suspended for the rest of the season due to domestic violence allegations.
Norris signed a minor-league contract with the Detroit Tigers after the end of the 2017 season before being released a few months later. In April 2018, he signed with the Sugar Land Skeeters, an independent league team. He became a free agent at the end of the season.
Norris made his MLB debut for the Athletics on June 21, 2012. He was called up to be a backup catcher behind offensively struggling catcher Kurt Suzuki. He went 0 for 3, but made a key defensive play in the ninth inning throwing out Dodgers Dee Gordon attempting to steal second base.[8] On June 24, 2012, the Athletics were trailing 1–2 against the San Francisco Giants when Norris hit his first career home run, and first career walk-off home run. The three-run home run helped the Athletics defeat the Giants, 4–2.[9][10] When Suzuki was traded to the Washington Nationals on August 3, Norris became the primary catcher for the team, backed up by the newly acquired George Kottaras.[11] Norris finished the 2012 season batting a slash line of .201/.276/.349, with 7 home runs across 209 at bats and 53 starts at catcher.[12]
In 2013, Norris was the primary catcher in a catching platoon, backed up by left-handed hitters John Jaso and Stephen Vogt.[13] Norris missed portions of August and September with a broken toe.[14] He started 71 games at catcher and played in 98 games overall, hitting a slash line of .246/.345/.409 with 9 home runs and 30 RBI.[12]
Norris was selected to play in the 2014 MLB All-Star Game, his first and only career appearance in an All-Star game.[15] He hit a slash line of .270/.361/.403 with 10 home runs across 385 at-bats, while making 93 starts at catcher with John Jaso as a back-up.[12] The Athletics would qualify for the postseason against the Kansas City Royals in the Wild Card game. The game lasted for 12 innings before the Athletics ultimately fell to the Royals, 8–9.[16]
On December 18, 2014, the Athletics traded Norris and Seth Streich to the San Diego Padres in exchange for R. J. Alvarez and Jesse Hahn.[17] Norris played in a career high 147 games in 2015, including 116 starts at catcher and 15 starts at first base. Despite moving to the National League, Norris racked up career highs in runs, RBIs, and home runs, and batted .250/.305/.404.[12] Defensively, he threw out 34% of would-be base stealers and his pitch-framing was reported to be much improved from previous years.[18][19]
In 2016, Norris struggled at the plate, posting a .186(career low)/.255/.328 slash line. Norris finished the season with 14 home runs, tying a career high, and 42 RBI.[12] Defensively, baserunners stole a league-leading 76 bases against him.[20][21] Despite the Padres pushing to trade Norris at the July 31 deadline, Norris remained with the team.[22]
On December 2, 2016, the Washington Nationals acquired Norris from the Padres in exchange for Pedro Avila.[20] Norris and the Nationals avoided arbitration over the winter, agreeing to a $4.2 million contract for 2017.[23] After the team signed free agent catcher Matt Wieters, the Nationals reportedly attempted to trade Norris but were unable to find a taker. The Nationals granted Norris his unconditional release on March 15, 2017, rendering him a free agent eligible to sign with any team and allowing the team to pay only one-sixth of Norris' 2017 salary.[24]
On March 25, 2017, Norris signed a one-year contract with the Tampa Bay Rays.[25] He was designated for assignment on June 23, 2017[26] and released two days later. In 2017 he batted .201/.258/.380 with 9 home runs.[12]
On September 1, 2017, Norris was suspended for the remainder of the 2017 season for violating MLB's personal conduct policy, regarding a domestic violence case against his former fiancée.[27] In an Instagram post, his former fiancée stated that Norris verbally and physically abused her and assaulted her in 2015. Norris denied the allegations and there was an investigation by MLB.[28][29] He did not appeal his suspension, and forfeited the remaining $100,000 that was owed to him by the Rays.[28]