Born in Brisbane, Queensland, Norman is of Māori descent. Norman played his junior football for the Beenleigh Lions and attended Keebra Park State High School on the Gold Coast before being signed by the Brisbane Broncos. Norman played for the Broncos NYC Team in 2009-2011, where in 2009 he was awarded as the Broncos Back of the Year. Norman is eligible to represent New Zealand.
In Round 1 of the 2010 NRL season, Norman made his NRL debut for the Brisbane Broncos against the North Queensland Cowboys, beating the likes of Josh Hoffman to the Number 1 jersey after impressing in the trials. Norman made an impression in the opening minutes by saving two early tries before for the 19th minute when he set up Israel Folau in the corner for the first try of the night. Three minutes later, Norman delivered a perfectly weighted pass to captain Darren Lockyer to send him over for the second try of the night which helped the Broncos stay in front for the rest of the game, eventually winning 30-24 at Suncorp Stadium. After the game, Norman was named Man of the Match and became an instant hit with Brisbane fans.
Norman continued to play at fullback till Round 5 before going back to the Broncos NYC team for a few matches after Hoffman was chosen to be the preferred fullback. In Round 9 against the Melbourne Storm, Norman scored his first NRL Career try in the Broncos 36-14 upset win in the Storms’ first match at their new home ground of AAMI Park. On 21 July, Norman extended his contract with the Broncos to the end of the 2012 season. For the remainder of the season, Norman only played in 5 matches, 4 of them at five-eighth as an experiment. He finished his debut year with 1 try from 12 matches. On 23 October, Norman played for the Junior Kangaroos against the Junior Kiwis, playing at five-eighth in both of the 2 junior test matches, the Kangaroos 24-16 win in the first and the 36-20 loss in the second test.
In the 2011 NRL season, Norman only played in 9 matches for the Broncos, playing most the year in the Toyota Cup.
On 24 February, Norman extended his contract with the Broncos to the end of the 2013 season. It was a breakout year for Norman, where he cemented the void five-eighth position following the retiring departure of Broncos captain Darren Lockyer. Norman played in all of the Broncos 25 matches, scoring 10 tries and kicking 2 goals.
Following the signing of Gold Coast Titans experienced playmaker Scott Prince to the Broncos, Norman was shifted back to fullback. On 25 March, Norman announced that he signed a lucrative 3-year contract with the Parramatta Eels starting from 2014, guaranteed fulltime playing position in his preferred five-eighth spot. Norman continued to play at fullback until Round 18 when he from favour of coach Anthony Griffin and spent the rest of the year playing for the Wynnum-Manly Seagulls in the Queensland Cup. He finished his last year with the Broncos with 2 tries from 18 matches
In February, Norman was selected in the Eels inaugural 2014 Auckland Nines squad. In Round 1, Norman made his club debut for the Eels against the New Zealand Warriors, playing at five-eighth and kicking 2 goals in the 36-16 win at Parramatta Stadium. In Round 10 against the St George Illawarra Dragons, he scored his first try for the Eels in the 36-0 win at Parramatta Stadium. Norman cemented the five-eighth position, playing in all of the club’s 24 matches and scoring 3 tries in 2014.
On 26 January, Norman played in the Auckland Nines and he was named in the Team of Tournament. In Round 13 against the North Queensland Cowboys, Norman played his 100th NRL match and also scored a try in the 36-30 loss, after they lead 30-6 till up to the 57th minute. Norman finished the season with 3 tries from 22 matches.
In February, Norman captained the Eels Auckland Nines squad.He took out coveted Player of the Tournament award after he led the team as they triumphed over the New Zealand Warriors 22-4 to win their maiden Auckland 9's title. In Round 1 against his former club the Broncos, Norman left the field injured and was seen using his mobile phone in the changing room, which is banned during NRL matches. Norman was cleared of wrong-doing and said that he was only letting his family know that he was okay.
During a round 9 game, commentator Phil Gould quoted, "Norman would walk into a blues Jersey if he was a New South Welshman." Norman's eligibility is to Queensland despite being stuck behind the likes of Johnathan Thurston and Cooper Cronk. By May, Norman was named third in the leader board for the Dally M Medal. On 21 July, Norman’s 2016 campaign ended after he was suspended for 8 weeks and was fined $20,000 for breaches of conduct including being caught with capsules of MDMA in his possession at the Star Casino, filming drug use and sexual activity and consorting with known criminals. He scored one try from his 18 appearances in 2016.
In February, Norman again captained the Eels Auckland Nines team. In Round 1 against the Manly-Warringah Sea Eagles, Norman made his return from suspension, shifting to halfback and scoring a try in the 20-12 win.
On 23 July 2017, Norman kicked a field goal to win the game for Parramatta in a close match against The Wests Tigers 17-16.