Yes you can make privacy on twister just you will have to do is to go on the setting of your twister page and click on protect my updates.
Through this you can easily protect your information regarding your profile page.
No one can see the profile page of your because of restrictions.
People makes fake id and they have habit of viewing of others profile pages in which they mostly see the pictures and friends on the others profile pages.
for that s reason twister has also given the privacy setting like the facebook has offered it many time ago through which only selected people can cheek your profile
i hope so this answer will help you a lot.