BuddyPress.org

You can use another plugin that requires to be invited via email, and once they register they can connect with WP-FB-Autoconnect. However, WP-FB-Autoconnect has been removed from WordPress.org, I’m not aware of what the reasoning was for that. If you’re wanting people to register and then be approved, you might want to consider putting up a form for them to apply & then you can send them the invitation through the plugin.

https://buddypress.org/community/groups/wordpress-mu-secure-invites/