I have an outlet that is supplied by 12x2 (no ground).
This is in a potentially wet area where I can easily run a 12x2 (with ground) from the load side of a near-by GFCI.
The problem is that I cannot get to the old 12x2 to completely remove it.
Is it OK to place wire caps on the line and neutral and leave them in the back of the outlet box?

You do not need to completely remove the old wire.

Why not just put a GFI in that box?

The old wire does not have a ground.
What would I do about the CFI ground connection.

Ignore it.
A GFI works fine without a ground, and it is even a legal and safe replacement for a non-grounding receptacle.

Yes, use a GFI. Note that some of the stickers that come with it are marked "no equipment ground"