As required by Apple's privacy policies, users with Apple devices have the option to permanently delete their account.  

 

BEWARE!  Account deletion is PERMANENT and there will be no way to recover the account, progress, or any purchased assets from the game.; nor can any assets be transferred to a new account.  Once the account is gone, it's gone!  Glu cannot restore deleted accounts. For this reason we strongly recommend securing your device against unauthorized use.

 

From the main screen, tap the gear icon:

 

 

Then tap the "Delete Account" button:

 

 

You will need to confirm your choice on the next screen: