Oxley joined Rotherham United as a youngster and was promoted to the club's first team during the 2007–08 season.
Hull City
After being scouted by several bigger clubs, he joined newly promoted Premier League club Hull City in August 2008 for a fee of £150,000. Oxley became the club's fifth choice goalkeeper, behind Boaz Myhill, Matt Duke, Tony Warner and Tom Woodhead. For the 2009–10 season, Oxley moved up to number four keeper at the KC Stadium, but was to be sent out on loan to Walsall in October 2009. He would only manage to make the bench for The Saddlers, and he departed a month later after failing to make a single appearance. On 25 February 2010, Oxley signed a one-month loan deal with Grimsby Town, becoming the third Hull player to be loaned out to Grimsby that season, following teammates Nicky Featherstone and Jamie Devitt. Oxley would go straight into the starting line up to face Dagenham & Redbridge on 27 February, after replacing regular number one Nick Colgan, who was rested by manager Neil Woods. The game ended in a 2–0 defeat for Grimsby, and when the club's next match against Shrewsbury Town came around, Oxley was dropped to the bench in favour of Colgan. On Friday 2 April 2010, Oxley rejoined Grimsby for a second loan spell, this time an emergency seven-day loan, following injuries to Nick Colgan and reserve Leigh Overton which left the club without a fit goalkeeper for their clash with Northampton Town. Oxley played in the 2–1 home defeat against Northampton, as well as the Easter Monday 3–2 victory over Accrington Stanley. Both Hull and Grimsby had suffered relegations by the end of the 2009–10 season. Following the sale of Boaz Myhill in the summer of 2010, Oxley was a regular on the bench for Hull in the 2010–11 season. On 26 October 2012, Oxley went on a month-long loan spell to Burton Albion, Although he had to return to Hull following a broken finger after some good performances for the Staffordshire club. On 12 January 2013 Oxley made his league debut for Hull when he came on as a substitute for Eldin Jakupović in the 3–1 loss at home to Sheffield Wednesday. Oxley signed a new two-year contract with the Tigers on 11 June 2013 following the club's promotion to the Premier League. In July 2013, Oldham Athletic signed Oxley on a season long loan, but was recalled on 27 March 2014. After spending the 2014–15 season on loan at Hibernian, Oxley was released by Hull City.
Hibernian
On 28 July 2014, Hibernian signed Oxley on a six-month loan, with a view to extending to the end of the season. Oxley scored with a clearance on his league debut for Hibs in a 2–1 win against Livingston on 9 August 2014, to become the first goalkeeper to score for Hibs since Andy Goram netted against Greenock Morton in 1988. When two of Hull's goalkeepers were injured in October 2014, manager Steve Bruce suggested that Oxley would be recalled to Hull, but this was prevented by international transfer regulations. It was confirmed in January 2015, that the loan to Hibs would be extended to the end of the 2014–15 season. In June 2015, he signed a two-year contract with Hibs. Oxley was the regular goalkeeper for most of the 2015–16 season, but lost his place to Conrad Logan near the end of the season. He was an unused substitute as Hibs won the 2016 Scottish Cup Final.
Southend United
Oxley signed a two-year contract with Southend United in July 2016. After a string of stunning performances during the 2017–18 season, Oxley was voted fans Player of the Season and Players' Player of the Season at the end of the campaign. On 4 June 2018 Oxley signed a new three-year contract at Southend. On 2 August 2018 Oxley was named as captain.
International career
Oxley has been capped at International level for both the England under-18 and England under-20 sides.
