Water – Any issue going from 3/8 to 1/2 copper

I think kitchen sinks are 3/8" (but I can never remember). So you'll want a 3/8" female, 1/4" male, 3/8" male tee. You should be able to find one at the local big box, or hardware store.

Something like this

1. Shut off the water using the shutoff valve.
2. Remove the existing supply line.
3. Attach the tee where the supply line used to be.
4. Connect the sink supply to the 3/8" male outlet on the tee.
5. Connect the refrigerator supply to the 1/4" outlet on the tee.

NOTE: Use your preferred pipe dope method (tape or goop), however, since it's a brass fitting dope should not be required.

If there's a valve, then turn it off and remove the pipe. If you're concerned the valve will leak, then shutoff the water to that line, remove the valve and cap the pipe there (or replace any T's with a straight fitting).

Leaving the pipe and capping the thin refrigerator line will be difficult and error prone, and you're still left with a valve and two places that may leak.