Oxford made his debut for the Hammers during the first leg of their Europa League first qualifying round against FC Lusitans on Thursday evening.
The 16-year-old defender played well against the Andorran side and was impressive during the 3-0 win at the Boleyn Ground.
The England Under-18 international captain normally plays as a centre-back, but on Thursday he featured as a midfielder.
Oxford became the youngster ever player to play for West Ham, breaking Billy Williams' 93-year record in the process.
Randolph was impressed with the performance of the teenager on his debut and was full of praise for him after the match.
“Reece [Oxford] has been very impressive all week in training,” the 28-year-old told West Ham’s official website. “He doesn’t look like a 16 year-old, he’s bigger than me!
“He is very strong and was not fazed by anything. If he keeps his head down and keeps working, there is no reason why he can’t go on to have a big future.”
It was a memorable debut performance from Oxford, who showed that he can be effective in midfield.
The youngster looked calm and confident when he had the ball at his feet, and also tried an ambitious effort on goal from 30 yards.