If you have authenticated the user. You should be able to use people.get
GET https://www.googleapis.com/plus/v1/people/me
response
"image": {
"url": "https://lh5.googleusercontent.com/-a1CWlFnA5xE/AAAAAAAAAAI/AAAAAAAAl1I/UcwPajZOuN4/photo.jpg?sz=50",
"isDefault": false
},
This will require that you have profile scope requested or one of these.
https://www.googleapis.com/auth/plus.login or https://www.googleapis.com/auth/plus.me
It will also require that the user created a google+ account. This is the only way to get the users profile picture unfortunately.
Option two is the people api which is linked to google contacts which may include the users profile picture if they added it. People.get
GET https://people.googleapis.com/v1/people/me?personFields=photos
Also returns
"url": "https://lh5.googleusercontent.com/-a1CWlFnA5xE/AAAAAAAAAAI/AAAAAAAAl1I/UcwPajZOuN4/s100/photo.jpg"