The 19-year-old has played one first-team game for the Lions since joining them from Irish club Bohemians in July.
"He's a player I came across when on a scouting mission a few weeks ago," Torquay player-manager Kevin Nicholson said. "It's a great opportunity for him to come and test himself."
Rooney could make his Gulls debut in Saturday's FA Trophy tie at Braintree.
National League club Torquay United have signed Millwall centre-back Paul Rooney on a 28-day youth loan.