Can you use a 12 volt 2 amp power source to replace your cordless drill battery?

This should work, but check a few things first. Make sure the power source is a DC source (Direct Current). Also check to see if the cordless drill has an operating Amperage less the 2A, because if it draws more than the source you will fry your power supply. If these fall within acceptable limits, just make sure you connect the (-) negative to the negative terminal where your battery was, and likewise for the (+) positive terminal. Its always good to have a fire extinguisher near by ;)