For adding a Facebook Login button in WordPress follow this article. I will show you how to add one-click registration and login with Facebook in WordPress. I used Nextend Facebook Connect plugin. Upon activation, go to "Settings > Nextend FB Connect" to configure the plugin App ID and App Secret Key.
Step One :
Log into your Facebook account. Go to developers.facebook.com “My Apps > Add a New App > Enter App Name + Email Address > Create App ID > complete captcha test > Submit”
Step Two :
Choose “Facebook Login > Set Up > Select the platform > Enter Site URL > Save”
Step Three :
Go to "Settings > Basic > App Domains > Privacy Policy URL > Terms of Service URL > Choose Category > Save changes"
Step Four :
Go to "App Review > Make Your app public"