Career
Youth Roberts began his youth career on the books at his hometown club Chirk Football Club before joining Tranmere Rovers at a relatively early age, in he was signed by Everton and would be part of the set up at Goodison Park for three years. In that time he was part of the development squads and Everton at both Under 18 and Under 21 levels. Roberts also featured in matches for the Everton XI alongside then youth players Ross Barkley and James Wallace but did not break through in similar fashion.
Burscough & Colwyn Bay loans
In 2011 Roberts was given the opportunity to gain first team experience at Northern Premier Division side Burscough.
Upon his return to Everton he was granted another loan, this time to Conference North side Colwyn Bay. He made 4 appearances for the North Wales side in 2011 before returning once more to Merseyside.
Cheltenham Town
Although he signed his first professional contract with Everton in 2011, a season later Roberts joined Cheltenham Town in 2012 after being released by the toffees. After a season at the Robins, Roberts failed to make an appearances, however he signed a new one-year contract in July 2013, keeping him at the club until the end of the 2013-2014 season.
On 3 May 2014, Roberts made his professional debut for Cheltenham in a 3-2 loss against Dagenham and Redbridge.
On 13 May 2014 after two years at Whaddon Road, Roberts was released by Cheltenham. He played in a second game for the Dragons in a 2-0 victory over his former club Colwyn Bay, where he kept a second consecutive clean sheet for Kevin Wilkin"s side, revealing he wanted to earn a contract at the Racecourse Ground. Chester
On 28 August 2014, Roberts signed for Conference Premier side Chester.
Bangor City
After being released from Chester, Connor Roberts joined Bangor City in the Welsh Premier League.
Connor Roberts is now considered one of the best Goalkeepers in the division along with Paul Harrison of TNS (The New Saints) and Ashley Morris of Bala Town, and many have suggested that Roberts could become the First player to represent Wales at senior Level whilst at a Welsh Premier League Club, due to the fact he was in the Wales squad not too long before joining Bangor City. Roberts qualifies for both Wales and Northern Ireland.
After progressing through the Wales under-17 and under-19 teams, Roberts made his debut for Wales under-21s in a 3–0 home friendly victory over Iceland in February 2013. In May 2014, he received a call up to the Wales senior squad for a friendly international against the Netherlands in early June.