My implant screw was wobbly for few days now has fallen out. It is a back molar. Can I just have it screwed back in?

please upload pic so i can guide u better, r u talking about healing screw of abutment screw? if healing screw, no need to worry. if abutment screw, visit yr dentist.

Uncertain if you are describing the healing cap or the actual restoration on the implant.  Either way, I would see your dentist immediately to address.  Hopefully it is a quick fix rather than an implant failure.

If it was the healing cap that has fallen out, it can be screwed back in by your dentist or your surgeon.  If your implant has come out, and this is very unlikely, it cannot be screwed back in.  If this is the case, you should immediately see your surgeon to evaluate the implant site, determine why the implant failed and propose appropriate care.

It sounds like the healing abutment used to keep the gums out of the implant has loosened up and come out.  This is an easy problem to resolve your dentist will need to screw it back in and maybe trim some overgrown gum.

yes, its a very simple proceedure, and they can come out, because they are not set with a torchimeter,  until you receive the final crown, the healing cap, can fall down, but put it in, as soon as posible, unfortunately you cant do it. because has a place for a screwdriver.