Young, 19, is an attacking player who can play anywhere across the front.
He joined the Cards in October after being released by SkyBet League One side AFC Wimbledon.
Woking`s academy manager Scott Harrison told the club`s website: "It's a good day for the academy, with another player joining the first-team environment. I have no doubt Reggie can progress and thrive, working on a daily basis with manager Anthony Limbrick and his coaching team".