Just grab some round fridge magnets and drop them on the corners of the baking paper. If you're using it on a metal baking pan, the magnets will hold the baking paper in place. They'll get hot in the oven though, so be careful about how you remove them once you're done.
The folks at ATK have a few other tips for keeping your baking paper from curling up. Hit the link below to see all of them.
3 Ways to Make Problematic Parchment Paper Stay Put [America's Test Kitchen]