The ex-Prez was stumping for Rev. Raphael Warnock -- who's running to maintain his Senate seat in a highly contested race -- when he started to lay out comparisons between the current Senator and Walker ... going on to crack jokes at the latter's expense.

Watch ... BO admits Walker was a football great once upon a time, but says that alone doesn't mean he should be considered for jobs he has no experience in -- stuff like flying an airplane or surgery -- and that common sense people would ask those basic questions.

Barack hilariously compares the sitch to him being hypothetically tapped to be a running back ... something he says he absolutely would be terrible at, and that no one would want him doing. In the same vein, he says HW shouldn't be taken seriously as a would-be Senator.

Walker's now-infamous badge moment during the debate was also poked at by 44 -- with Barack likening it to playing cops and robbers. The crowd was busting up at his jokes.

For his part, Walker didn't find it funny ... but did fire back at the former President in his own campaign speech Saturday. He insisted he wasn't a celebrity, but rather ... a "warrior for God." Walker also went on to say Obama's been absent while he's been on the front lines.