Open settings and click the button at the top of the list with your name on it. This should open a page with your Apple ID settings. Hover your mouse over your current profile picture and an edit button should show. Click on it.
If this doesn't work go onto safari (or any browser) and type in iCloud.com, log in. Once you do this a home page should pop up with a series of widgets. The first widget should show your name and current profile picture, click this widget. A webpage will popup. At the top right of this webpage, under your email, it will say photo. Click 'Change Apple ID Photo'. This will create a popup that you have to scroll to the bottom of. When you see the blue text that says 'Browse your device for a new image, click it. Problem solved.