How to make User Picture a required field?
You can do it by using these modules :

Register with Picture


  
  Install and enable the module
  Navigate to: Configuration -> Account Settings. (admin/config/people/accounts)
  Check Enable user pictures if it isn't checked already.
  Confirm Enable pictures on registration is checked.
  Use the Registration Picture Field Weight field to adjust the display order of the picture field on the registration form. It can be
  a negative or positive number.
  


user picture field


  1, Add a image field to user, for example "field_user_avatar"
  
  2,config this field,and make it show on user register form.
  
  3,install this module, navigate to
  "admin/config/people/user_picture_field", here you can config the
  "Machine name of source field that used as user picture"
  
  When user register an account, he/she upload an image through image
  field "field_user_avatar", this image will be used as user's
  picture(avatar).