What is the current carrier in copper wire?

Your question makes no sense. If you want to speak in terms at the Atomic level, then the "Free Electrons" moving, pushed by the Voltage, through the wire would be an answer.

A smart*** answer would be the copper wire because it is a good conductor. The best conductor is Silver next would be Gold, then Copper and finally Aluminium.

This is obviously a test or home work question.
We will not do your home work for you. Why not tell us what you think the answer is and we can discuss it.

At the same time, the question makes no sense. What context is it being asked?