Is there anyway to authenticate a user with Github without redirecting them within the current page?
github, oauth-2.0
Solution
The answer to the question as framed is "use a different grant flow" but your questions tell me you don't understand OAuth grant flows so you may be better served by a lecture on OAuth.
Popups and iframes are specifically designed to prevent code running outside them from fishing out data, because if you could do it so could invisible iframes in dodgy ads. Give up on that approach because in the unlikely event that you find a way, browser makers will immediately take steps to prevent your solution from working.
The behaviour you describe sounds to me like implicit grant flow.
Here's a walkthrough of the various ways OAuth2 can work.
Why so many ways?
Implicit grant is a flow that uses redirection to deliberately take control away from your code - which might be compromised or impersonated - and give it to a trusted third party, the OAuth provider: GitHub in this case. You pre-register the point to which control is returned after authentication, the point of which is the token is always given to your code.
Amnesia, popups, and what was I doing before we were so rudely interrupted?
There are flows that use popups. Usually this is the authorisation code grant flow. Popups are not suitable for mobile devices and this led to the creation of the implicit grant flow.
The usual reason for not liking redirection is the amnesia it causes. The solution is to store app state persistently prior to passing control to the OAuth provider, and to write a return-from-oauth handler that unpacks the JWT from the redirect parameter and then restores the app state you saved.
Note to self
If the user is anonymous prior to authentication serialise your state to a string and put it in a cookie or in localStorage.
If the user is not anonymous and is authenticating to elevate privilege you'll have to send any privileged data to the server and just persist a retrieval token on the browser. You must ensure that retrieval of this state requires both a valid OAuth token and a valid state token, and that it discards the state after honouring a request so that a replay attack will be conspicuous (you'll have to handle the fallout).
Having acquired a valid token you can use it to request profile information from GitHub. A very small amount may already be present in the JWT; you'll probably have the email address that served as a login, but this isn't necessarily the right one for correspondence.
GitHub OAuth documentation
It appears GitHub only supports code grant auth. That means you have to do the popup/iframe thing. Here's their doco:
https://developer.github.com/v3/oauth/
Code grant - why?
This flow doesn't give you an encoded token, it gives you a code you can redeem for an encoded token. The idea is that when the token expires you can use the code to get a refresh token without sending credentials over the wire.
Problem
I am looking to allow a user to sign in with github for a website I am creating that will be API driven. However, I am running into a problem that there seems to be no way of authenticating a user and getting their email and name without redirecting them on the current page to github. I have tried to create a popup, but there is no way for me to get the necessary data from the popup, namely an api token to be used for the next calls.