I'm pretty sure you can only become sworn to the God-King if you main as Fane. The Voidwoken at the entrance to the academy offers you this choice. You may want to not dig deeper into this, so you don't get spoiled.
In my case I was playing custom character, female human undead.
At academy I had an option to become sworn.
But the game is funny - sometimes they called me Fane (due undead), sometimes Lohse (due human female)
