The 19-year-old made his Reds debut in 2010 when he became the youngster player to ever appear for the club's senior side against Hull.
Robinson has made 11 appearances in total for the Merseyside outfit with his most recent outing coming in the 3-2 FA Cup defeat to Oldham last month.
The teenager could make his debut for Dean Saunders' side against Barnsley on Tuesday as the Welshman looks to finally secure his first win as manager.
Saunders told the club's official website: "Jack is left-footed and he can play anywhere down the left side and he gives us competition for places.
"I spoke to (Liverpool manager) Brendan Rodgers, I spoke to Steve Cooper, who was his coach in the Under-16s and 17s, and I've spoken to nearly all the coaches that he's played for and all of them have been very positive about him.
"He's got really good quality on the ball, he's aggressive and he's a winner.
"Sometimes a young lad and a fresh face comes in and lifts the place, and I think Jack is strong enough to be able to deal with the pressure."