REPUBLIC OF IRELAND
Randolph has represented the Republic of Ireland at U15, U16, U17, U18, U19,U21, B, and senior levels. He was called up to the Republic of Ireland senior squad for the first time in March 2011 for a match against Macedonia. He was again called up in May, and made his full international debut in a friendly against Oman on 11 September 2012, coming on as a substitute in a 4–1 win. His second Republic of Ireland appearance was against Spain on 12 June 2013, again as a substitute; he made a "brilliant fingertip save" from Santi Cazorla before conceding a late goal by Juan Mata as Spain won 2–0. On 8 October 2015, Randolph replaced Shay Given in the 44th minute against Germany in a 2016 European Championship qualifying match and provided the long ball assist for Shane Long's winner in the 70th minute in a match won 1–0 by the Republic of Ireland. Randolph played every match for the Republic of Ireland at Euro 2016, against Sweden, Belgium and Italy before being defeated by France.
On 30 May 2015, West Ham United confirmed that Randolph would join the club on 1 July when his contract with Birmingham expired. He made his debut on 2 July in a 3–0 victory over Lusitanos in a Europa League qualifying match.
Randolph made his league debut for West Ham in a 4–3 home defeat to Bournemouth on 22 August 2015. He continued in goal, and kept a clean sheet in a 3–0 win against Liverpool on 29 August which was West Ham's first league win at Anfield since 1963. Randolph played in West Ham's last three matches of the 2015–16 season which included their final match at the Boleyn Ground, a 3–2 victory over Manchester United. He played in 15 matches in all competitions over the season. In July 2016, Randolph signed a new, four-year contract with West Ham. Following a goalkeeping error by first choice goalkeeper, Adrián, in a match against Stoke City in November 2016, Randolph became West Ham's regular goalkeeper.
In January 2020 Randolph returned to West Ham United FC.
Having progressed through the youth ranks at Ardmore Rovers and Premier League club Charlton Athletic, Randolph turned professional in 2004 with Charlton. He spent time on loan at Welling United, Accrington Stanley and Gillingham before making his Charlton debut in the last match of the 2006–07 season.
Having made 20 appearances for Charlton, he moved on to Scottish Premier League side Motherwell in July 2010. He played regularly for Motherwell over three years, then returned to England to join Birmingham City, for whom he missed only one Championship match in two seasons. He signed for West Ham United in 2015 and Middlesbrough two years later. Randolph has re-signed with Premier League side West Ham in January 2020.
n 2006, Randolph made ten appearances for the Republic of Ireland under-21 side, and a single appearance for the Republic of Ireland B team. He made his full international debut for the Republic of Ireland in September 2012 where he has been a main fixture ever since.
In 2019 he was awarded with both the Middlesbrough Fans' and Players' Player of the Year awards.