Like nearly everything Ron owns, Scabbers is secondhand and a bit battered (PA4).
From the comments made by Ron on the Hogwarts Express that September, it would seem that Ron received Scabbers from Percy when Percy was given his owl upon being made Prefect. Assuming that Ron and his brothers received their Hogwarts letters at the same time that Harry would have received his, had Uncle Vernon not intervened, then we know that Percy was made Prefect on July 24. Sometime after that, Molly and Arthur bought Percy his new owl, Hermes. This may very well have been when the Weasleys came to Diagon Alley to buy their school things.
Scabbers may have been comparatively neglected under Percy's ownership, since it seems very unlikely that Percy of all people would bring a pet rat to school with him despite rats not being one of the kinds of pets listed as approved. -BB