You can send a Twitter private message, also known as a direct message, without being followed by the recipient. However, you must first follow the recipient of the message. Send the direct message to the individual, and then block the user’s account if you don't want him to follow you. The user isn't notified when you block him, but he won't be able to see your tweets or profile information.
Send Direct Message
Follow the user you want to message by opening his Twitter profile then clicking the “Follow” button. To message the user, open your timeline page and type the letter “d” followed by a space, then the user’s Twitter handle in the Compose box. Type your private message after the user’s handle, and then click “Tweet” to send the message. After you send the direct message, block the user to prevent him from following you.
After sending the private message, open the user’s profile page. Click the arrow next to the person icon, and then click “Block (@username).” The user is unable to follow you now. The direct message you sent is not affected by blocking the user. He will receive and be able to view the message. Your account automatically unfollows the user once you block him.