Bardsley seemed to be on his way out of Sunderland when his late night visits to casinos came to light.
He then appeared to mock the club, but will be given a chance to redeem himself under the new boss.
"I have decided, with the backing of the club of course, that [Bardsley] is a part of the club and he is available to play," Poyet told The Shields Gazette.
"I ask the fans, with respect, to please give him a chance because he could be very, very important for us.
"He is very happy to have another chance. He knows what he did was wrong but it's in the past so lets all try and put it behind us."
Bardsley could feature against Swansea City this weekend after recovering from a broken foot.