Wormtail had the Dark Mark and everything, which means he was in Voldemort's inner circle.
This itself is strange already, as we see in Goblet that Voldemort is very condescending towards Wormtail for his talentlessness despite having taken care of him for the whole year, and helping him out with his elaborate plot against Harry.
Since Wormtail was more friendly with the Marauders since his school years, I would assume it would take him quite some time to gain enough trust with Voldemort to get the high honour of being branded with the Dark Mark.
In the 3rd book Sirius says that Wormtail had been hiding from Voldemort's old supporters in Azkaban because they all thought he double-crossed Voldemort, as he met his downfall at the Potter's on Wormtail's information.
Keeping in mind that Voldemort likes to work alone and in secrecy as much as possible (in Goblet, during the trial of Karkaroff scene, he mentions that only Voldemort knew the true identities of all the DE's and even fellow DE's did not always know each other), that many DE's in Azkaban knew that Voldemort had gone to the Potter's on Wormtail's information indicates that Wormtail had been with Voldemort for quite some time by then.
The fact that he didn't know Wormtail was a Death Eater is the reason given for him not taking a more direct approach in protecting Lily, and not alerting Dumbledore to the fact that there was a traitor in their midst, when he went to beg Dumbledore to protect Lily.
So the question is, when exactly did Wormtail become a Death Eater? He must have been with Voldemort for quite a while by the time Voldemort went to attack the Potters, but if this was true Snape should have known about it and alerted Dumbledore.
(This probably has no canon answer, so any extrapolation based on canon information is more than welcome)