Is there an adapter that will fit the Gorillapod screw to my compact Sony camera (the camera's hole is too small)

Which model Sony do you have?

Unfortunately, some of the ultra compact Sony cameras are among the very few in the world which do not have a standard 1/4-20 tripod mount.

A few Sony cameras (like the DSC-T7) come with an included tripod adapter plate which lets you attach it to a regular tripod screw. If yours has a tiny hole on the bottom, it probably is capable of accepting this kind of adapter. You'd probably need to find a Sony reseller to purchase it, however.

The Gorillapods come with a universal 1/4-20 tripod screw, which will fit virtually every other camera out there, and should work with the Sony adapter plate if you get one for your camera. Good luck!