You cannot simply log the user into Canvas.
You could use the OAuth flow to get an access and refresh tokens. This will require the user to authorise your application via the browser. Once you have the access token, you can generate an URL that will log them into Canvas, and optionally send them to a specific page (OAuth2 Endpoints - Canvas LMS REST API Documentation ).
If you store the user/refresh token, your application could then log them in the future without going through the OAuth flow again.