Is there any way to add Apple Care for damage to your phone?

Welcome, thee112, to Apple Support Communities.

You have only a limited time for adding any Apple Care to your purchase.

How long has it been since you purchased the phone in question?

Applecare plus is an extended warranty.

It has to be bought within 60 days of the original purchase of the device.

You can't buy Applecare plus after you have damaged the phone, that would be fraud.