Norman previously played for the Brisbane Broncos, the Parramatta Eels and St. George Illawarra Dragons in the NRL and Toulouse Olympique in the Super League.

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.

[14] It was a breakout year for Norman, where he cemented the void five-eighth position following the retiring departure of Broncos captain Darren Lockyer.

Following the signing of Gold Coast Titans experienced playmaker Scott Prince to the Broncos, Norman was shifted back to fullback.

[17][18] 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.

[27] 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.

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.

[29] 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.

[32] 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.

On 22 May, coach Brad Arthur shifted Norman to fullback in a switch with Clint Gutherson for the Round 12 clash against The Brisbane Broncos.

[42] On 15 January, a video emerged online through social media showing Norman and Australian Rugby Union player Kurtley Beale sitting on a couch as an older man is shown snorting cocaine off a plate.

In the second half and with only a minute remaining, the game was set to head into golden point extra-time to decide who would be the series winner until New South Wales shifted the ball to the wing of Blake Ferguson.

[47][48] Norman made a total of 19 appearances for St. George Illawarra in his first year at the club as they endured one of the worst ever seasons finishing in 15th place.

Before the start of the season, St George Illawarra were expected to reach the finals and challenge for the premiership but only managed to win a total of 7 games.

[54] In round 16, Norman kicked the winning field goal for the club as they beat the New Zealand Warriors 19-18 in golden point extra-time.

[56] Norman played a total of 22 matches for St. George Illawarra in the 2021 NRL season as the club finished 11th on the table and missed out on the finals.

[58] Going back on his decision to retire, Norman signed for France based Super League side Toulouse Olympique on 20 April 2022.

[59] In round 18 of the 2022 Super League season, Norman was awarded the man of the match in Toulouse Olympique's 38-26 victory over Wakefield Trinity at Magic Weekend.

[62] Following Toulouse Olympique's relegation from the Super League, Norman signed a one-year contract to join French Elite 1 side FC Lézignan XIII.