How to Protect Your Tweets
Next to canceling your account, protecting your tweets is the best way to keep your privacy on Twitter. Protecting your tweets can be done in a matter of seconds, and prevents anyone who has not been pre-approved from viewing your tweets.
First and foremost, make sure you're logged into your Twitter account. At the top of your Twitter home page, click on "settings."
In the settings window, scroll down until you find the setting that says "Tweet Privacy." There will be a small check box that says "Protect my tweets."
Check the box and then click "save" at the bottom of the screen, which will then ask you for your password to save the changes. Enter your password when prompted.
Now, when someone tries to follow you, you'll be alerted via email, which will give you an approve or deny option. Now you're as protected as you can be! Keep in mind, this means you have to make sure you don't approve anyone that you want to keep out of your tweets. It also means that if you tweet at someone that you haven't approved, such as a favorite celebrity, they won't see it.