Set user role based on invitation code

This is one way to do it

add_action('user_register', 'set_custom_default_role')
function set_custom_default_role($user_id) {
    // Maybe get available referral codes from database & compare them against the one available
    if(true) {
        $user = new WP_User( $user_id );
        $user->set_role('custom-role-slug');
    }
}