My guess is that it descended from "rascal", or is closely related. I know a lot of French and some Spanish and Italian, and I don't think "rascal" appears in those languages, so it can't come from Latin/Greek. But, it doesn't sound Anglo Saxon or Germanic, so I reckon it might be Shakespearian, he introduced loads of new words like this.

Edit: I have just googled, I was mostly wrong. "Rascal" comes from Latin through old French, then "rapscallion" evolved in English in the 17th century to be able to add spoken emphasis. It's just easier to contemptuously spit "you rapscallion" than "you rascal".