According to the comparison of measurements by 9to5Mac, they note that the iPhone 13 across the various models are thicker ever so slightly by 0.01-inches, thanks to the new cameras in the iPhone 13 models that has resulted in a larger camera bump. If there was no bump, we imagine that you could probably squeeze the phone into an iPhone 12 case.
However, as the bump does stick out quite a bit and since cases need to have a cutout to support it, there is a good chance it won’t work. Maybe, just maybe, there could be some third-party cases that have slightly more leeway and give, so you could try your luck, although we don’t necessarily recommend it.
This is because if it is such a tight fit, trying to squeeze it in could apply unwanted pressure which could potentially crack the glass or damage the lens, so for now, it looks like you’ll have no choice but to spring for a brand new case instead of upcycling your old one.