This is free Q2A plugin that allows users to invite their Facebook friends to Q2A.
Requirements: if you have not got a facebook app yet, first go to facebook developers page and create a new app. Do not forget to set the app's category as "Games".
Installation: Plugin the plugin folder into qa-plugin directory. Go to Admin/Plugins set your configurations, then go to Admin/Layout add the FBinviter widget to sidepanel.