Your profile picture can be either a randomly given game avatar (which cannot be changed by you) or your Facebook profile picture. To choose your Facebook picture as your game avatar, you will need to link your account to Facebook.
You can only change your game profile picture for one of your choice by changing your Facebook profile picture. If you want to link your account to Facebook without showing your profile picture, you can do so by going to Menu > Settings > Facebook and removing the checkmark from the tick box. There, you can also control whether to show your Facebook username or post your game activity on your Facebook feed.