In March 2012, it was announced that Cameron Norman, a versatile right-sided defender / midfielder from Sprowston, would be joining the Canaries as an Academy Scholar in the summer of 2012. He joined the Canaries at the age of 10.

Norman played in both FA Youth Cup semi-final matches against Notts Forest which the Canaries won to progess to the FA Youth Cup final but was sent-off in the second leg. He also played in both legs of the final which the Canaries won 1-0 and 3-2 against Chelsea to secure victory in the FA Youth Cup for the first time in 30 years.

On 13th May 2014, Norman signed a two year professional contract with Norwich

On 29th October 2015, Norman joined Conference side Woking on a one month youth loan. This was extended to January 2016.

On 10th June 2016, Norwich announced that they woiuld not be renewing Cameron's contract.

In September 2016, he joined Norwich United debuting against Waltham Abbey in the Ryman League on 25th September 2016.

At the end of October 2016, Norman joined Concord Rangers of the Conference South and made his debut on 29th October in a 2-2 draw with Chelmsford. He made 14 appearances for Concord Rangers, scoring once.

On 7th August 2017, Norman signed for Kings Lynn Town. In February 2018, it wasd reported that his fine form for Lynn had generated interest from Football League clubs. He has spent time on trial with Northampton Town who, along with Portsmouth, Oxford United and Doncaster Rovers are said to be keen on signing him.

After helping Kings Lynn reach the Southern League play-off final in May 2018, Norman left the Linnets and signed for Oxford United on 18th May 2018

On 18th January 2019, Norman signed for Walsall for an undisclosed fee on a two-and-a-half-year deal. He had played 12 games for Oxford. Norman made 9 appearances for Walsall in 2018/19 but they were relegated to League Two on the final day of the season following a goalless draw with Shrewsbury.

He was released by Walsall, along with seven teammates, on 12th May 2021.He had played 72 games for Walsall scoring once.

On 4th June 2021 he signed for Newport County on a two year contract.

Normann left Newport on 13th June 2023 rejecting a fresh contract from the Exiles. He had played 100 games for them.

He signed for MK Dons on 16th June 2023. "He has an excellent playing record over the last few years and he will give us a real attacking threat from a defensive position" said head coach Graham Alexander.

On 27th June 2024 he signed for Tranmere Rovers on a two year deal.