He at least does by the time of Voldemort's second rising - as Voldemort touches it to call the other Death Eaters. I really don't know if he's had it before then though.. I suppose it would make sense though. I'm not sure that Voldemort could have had the strength to put the Mark there in his half-alive-form. But then again, he was strong enough to hold a wand and kill the gardener at the Riddle house.
It just seems most logical to me that once Peter gave Lily and James' position to Voldemort, he would have been given the Dark Mark. For Peter, betraying his friends would have been to show where his loyalty was - if Voldemort had succeeded. So perhaps that was his last task before he was worthy of the Mark in Voldemorts eyes. He would probably have given him the Mark before he went to the Potters so that Peter can celebrate Voldemort's Victory properly with all the other true DE's.
It just feels like this makes most sense to me. Seeing how (in Voldemort's eyes at that point) Peter gave him the most relevant information to fulfil the prophecy and kill Harry, he probably did deserve the Dark Mark.