Randolph made his first-team debut for the already relegated Charlton in their last match of the 2006–07 Premier League season, away against Liverpool. Replacing loanee Scott Carson, who was ineligible to play against his parent club, Randolph performed well, limiting Liverpool to two goals, one of which was a penalty kick in the 90th minute for a 2–2 draw. He was second-choice behind Nicky Weaver in 2007–08, and in February 2008, joined Bury of League Two on loan. After featuring 14 times, Randolph was recalled by Charlton to cover for Weaver, who was sent off in a match against Plymouth Argyle. He started Charlton's next match, at home to Southampton, and contributed to a farcical own goal when he appeared to catch a high ball, then dropped it into the net via teammate Paddy McCarthy.