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 IRREVERSIBLE 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, access the Settings screen:

Tap the "Delete Account" button

The next screen will ask you to confirm.