An option is available to show a “join our affiliate program” checkbox on the store checkout when creating an order, for non-affiliate users.
This will only show if the user does not already have an affiliate coupon assigned to them. They must also be logged in, or have the “Create an account?” checkbox checked for it to show.
Here’s a look at the settings:
These settings can be found under “Registration” tab in the plugin settings page, when registrations are enabled.