When Pettigrew killed all those people and blamed it on Sirius, he turned into a rat to escape. That was his animagus. While he was a rat he went running off to the sewers. He went from Diagon Alley (where he framed Sirius) all the way to the Burrow. Percy, (still a young child) was fascinated with rats and when he saw Pettigrew, he jumped at the chance to keep him. Of course Pettigrew had to go along with it otherwise he would get caught. In the end he enjoyed being a rat, and became the family rat for many years.