What you are describing is called a "saddle valve".
I'm assuming you are saying that the drip is coming from the vicinity of the valve and not from your leaking GE profile fridge, though your description wasn't that specific.\
If it is from the valve:
Chances are the rubber washer which seals the body of the valve against the surface of the pipe has dried up and shrunk, or rotted out.
You can try tightening the screw(s) which hold the valve onto the pipe to see if that squeezes the washer enough to make it seal again.
If it doesn't, and since you say you don't want to fix the fridge, you could just remove the saddle valve and block the hole in the pipe with a clamp type pipe patch. (This ssuming you don't have the tools and experience to tackle a full blown soldered slip coupling repair.)
HTH,
Jeff