You can access your (or really any user's) profile photo by visiting the GitHub
profile URL with .png added on to the end.
So, my GitHub profile URL is:
https://github.com/jbranchaud
If I were to add .png on to that and visit it in my browser:
https://github.com/jbranchaud.png
I'd be redirected to the following URL:
https://avatars.githubusercontent.com/u/694063?v=4
This is the stable URL for my GitHub avatar. In the browser I will see the full resolution image which I can download as needed.