The actor has taken to the stage with Beck multiple times this week and was seen greeting fans and drinking in a Newcastle pub with Sam Fender on Wednesday.
His activities come shortly after jurors in Virginia returned a favourable verdict toward him in his multi-million dollar defamation case against former partner Amber Heard.
Social media posts from the Folly Wildlife Rescue centre in Tunbridge Wells, Kent, social media showed Mr Depp with the animal, named Freddie Mercury.
He was dressed in a military-style jacket over a checked shirt and wore a peaked cap and dark glasses.
“Guess who’s been to see us at Folly Wildlife Rescue – no, you’re not seeing things- that’s the real Johnny Depp,” the post read.
“As you probably know, Johnny has been appearing with our patron Jeff Beck on his UK tour and in a recent break, Jeff’s wife Sandra brought him up to visit us and see for himself the work we do with wildlife.
“And what an incredible afternoon it was for our staff and volunteers, as he toured the hospital’s care and vet units.
“Johnny was incredibly complementary and in his own words ‘blown away’ by what he saw.
It continued: “To top the visit off, we even allowed him the rare privilege of briefly holding Freddie (as in Mercury!) one of the many orphaned badger cubs we’re currently hand rearing.
“I think it’s fair to say he was bowled over by the whole experience.”
It comes as Depp was confirmed to be joining Beck for the remainder of his UK tour.
The actor, who collaborated with Beck on the 2020 track Isolation, previously surprised audiences and fans when he joined the musician on stage in Sheffield and at London’s Royal Albert Hall.
He will now perform in Gateshead, Glasgow, Manchester, Birmingham and York.