Doubt it'd even have one? While lots of firearms manufacturers used some sort of a serial number system, they weren't required until the late 60s.
Remington serial #ed all their rifles, I have a M24 Gallery Gun that was built in the early '20s, and it's a got a serial #. The Model 12's # is probably on the tang or under the front of the receiver, like my M24.
Dad's old Stevens 86D, which I have now, isn't numbered anywhere except for some patent numbers which don't illuminate when it was made. I'm guessing it was made in the mid to late '30s.