Yes, you can password protect any directories and files placed within them. To do that, please follow these steps:
Login into your cPanel and click on the "Password Protect Directories" icon, under "Security section" of cPanel. From a list of the directories select the name of the directory you wish to limit access to. On the new page, please create a username and password. Just fill in the username and password for the username. Next, check the box next to "Password protect this directory"; Write a warning message in the "name the protected directory" filed. This is the message that will be shown when someone tries to login in the protected directory. Click on save button below.
Congratulations, the directory you selected is now protected by a password!