Short answer: probably not. Apple has a sneaky habit of ever-so-slightly tweaking the dimensions of its devices between generations. Not enough for you to notice in everyday use, but sufficient to mean your old case doesn’t slip neatly over your brand-spanking new smartphone.
And it’s the same story for the iPhone 13. While the height and width dimensions are the same as the iPhone 12, each model in the line-up is a sliver thicker (0.15mm). While that alone would rule out most slim-fitting cases, Apple has also shifted the buttons further down the side of the iPhone 13.
And just to make sure your iPhone 12 case doesn’t fit right, the rear camera bump has grown in size – most noticeably on the iPhone 13 Pro, where it’s substantially larger than its predecessor. So unless you’re willing to go full DIY and refashion your existing case, you’ll need to start shopping.