Can I simply connect a wire (copper) to the back of the fridge by a pre-existing screw and connect to the outside of the socket box to the screw that keeps the cover on

Of course you can. But doesn't the refrigerator have a grounded plug already?

No, I got it from my grandmother... its one with the oval front, the super old kind. I'm guessing its from the 50's. I plugged it in once and I got shocked about a half hour later. I realized by not thinking that its only a two prong cord

Hmm... not a safe situation. I take it the cord isn't polarized either, meaning inserting it the wrong way is how you got your shock... consider a newer unit or have someone rewire it to provide polarization, and proper ground.

How about NO YOU CANT!

Either get this thing fixed or don't use it!!

Or at least plug it into a GFI protected receptacle so you don't DIE!