Richardson, 21, spent two months at the Britannia Stadium last season, making seven appearances for City and is happy to be back in the Midlands.
He told the club's official website: "It's great to be back at such a great club and I'm really looking forward to this month here.
"I really enjoyed my time here last season and I hope I can play as well this time around.
"There are many new faces as well as familiar ones and I can't wait to get playing for Stoke City again."