Yes, you can quitclaim a property to your relative and then he can pay the real-estate taxes. You can also come to a settlement as to who will pay the tax. If you decide to pay the tax but are unable to pay it, then the tax department can ask your relative to pay the tax as the property is in his name. At that point in order to save the house, he will have to pay the taxes.
The person who owns the property will have to pay the real estate taxes. Once you quitclaim the property to your relative, henceforth he will be responsible for paying the taxes.