Yes, with some quick setup users can quickly login via Facebook to write a comment.
Enable Facebook Login with the free JetPack Plugin
This is the easiest method for enabling quick Facebook login for your comment form. By using this method users can login via multiple methods instead of just Facebook. And the comments continue to be managed inside of your blog admin.
Login to your blog admin and go to Plugins. (Advance Blog Users: Choose Plugins > Add New. Search for Jetpack by Wordpress.com and install the plugin)
Activate the plugin. Once activated you'll be prompted to create a free account on Wordpress.com (create this account to continue)
In the Wordpress admin sidebar go to Jetpack > Settings then click on Engagement settings. Scroll down and activate the Comments setting to enable login via Facebook, Wordpress.com, Twitter and Google +
4. Users will then be able to quickly login on your comment form with any of those social media accounts, including Facebook.