I have about 70 feet of 10/2 wire left over and needed to add a light in my kitchen. I ran out of 12/2 and was wondering if 10/2 would work or not.

Sure it will work, if you did not already own it we'd tell you it is overkill. 10-2 can handle 30 amp and it appears you have ben using 12-2 or 20 amp rated wire.

One issue using # 10-2 cable for a 20 amp circuit extension is #10 wire will need use more space in electrical boxes and may or may not be allowed in any existing boxes.

At least 6 inches of wire is required in each box, and if the box is too small, most times the wire is incorrectly cut shorter to get the wires in the box.

Save the 10-2 for something else, Temporary Generator power or something. I would stick with the 12-2.
I am a believer of Overkill, but not for this.

I am totally with TK and Strat on this.

There is no valid reason to use this #10 for this. Just get the proper wire, you'll be glad you did.