This problem is most likely connected to your Facebook privacy settings.
Please open your Facebook Homepage and go with the mouse on the Ratsapp on the left side. Click the cogwheel and select "Edit settings". At the top you will see the option "App visibility".
Please select "Friends" in the drop down menu. Now you should see your Facebook friends who are already playing the game in the friends window of the app. With the "invite" button you can invite more Facebook friends to the game.