It should work if you log in to Facebook in your Settings app. This can also be helpful to some other Facebook features.
Tap your Apple Settings app. Scroll down to Facebook and tap that. There will be a place for you to enter your Facebook username and password. After doing that you should be able to log in to Word Chums. Sorry for this inconvenience and thanks for playing!
If you are already signed in to Facebook in Settings the following can apply:
If you said "No" to connect to Facebook at some point you may have to go to the Apple Settings app to allow access.
From the iPhone/iPad home screen, go to the Settings App, and scroll down to Facebook, and then to the "Allow these Apps to use your Account" list, and make sure Word Chums is set to ON.
If there is still a problem...tap settings on top right of Word Chums main screen. Then scroll down and see if there is a disconnect Facebook option. Tap that and then hit Connect Facebook to reset the connection.