I figured out the way to do this. It is done through the Steam link button in the account page: https://screeps.com/a/#!/account

It's a bit confusing, however, that the steam app has a way to sign in that is not functional in this case.

Is it possible to get my benefits from purchasing on steam if I previously created my account at screeps.com? When I try to use my existing account in the steam app, I get sent to the register page where the reCaptcha shows an error. There is also a loading indicator that doesn't go away which makes it seem there's some kind of error behind the scenes.