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.

To delete your account, access the setting screen by tapping the gear icon in the upper right of your main screen.

Wait a few moments for the  "Delete Account" button to appear, and tap it.

Type the word "CONFIRM" in the text box and then tap "Delete Account."