Can I replace my iPhone for a new one with Apple Care?

Sorry to hear about your phone. Assuming that you have not had more than two accident damage claims within the past twelve months then your phone will be repaired or replaced. Also, if the damage is deemed 'cosmetic' then it may not be covered, such as scratches or minor physical damage.

AppleCare Products - iPhone - Apple

Click on the Contact Support link at the top right of this page to start the service process and make an appointment. If you purchased AppleCare + and this is accidental damage you will have to pay your deductible. If you have the standard one year warranty you will have to pay for an out-of-warranty replacement.

What device?

Do you have AppleCare Plus?

You can check by going to here -> https://checkcoverage.apple.com

An Apple Retail Store, an Apple Authorized Reseller, or AppleCare (online) can facilitate the repair under the AppleCare+ protection plan.