Yes you can check, who is added user in SharePoint group by collecting audit data. If you want to fetch these reports using PowerShell, Please follow this earlier discussion : http://sharepoint.stackexchange.com/questions/96491/report-on-who-added-user-to-sharepoint-group-and-when/96497
If you wish to get the reports into real time, Lepide SharePoint auditing tool should be useful for your purpose. It helps to track every critical changes into real time and provides the reports at granular level.
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