Short answer: No, AppLocker is not supported on Windows Server 2012 Server Core.
Slightly more long-winded answer:
My Google/Bing mojo failed to find a definitive answer to this question on-line. In fact, I found two apparently conflicting sources of information.
This was the first one:
Windows PowerShell can used to manage AppLocker on Server Core installations using the AppLocker cmdlets and, if administered within a GPO, the Group Policy cmdlets. For more information, see the AppLocker PowerShell Command Reference.
http://technet.microsoft.com/en-us/library/hh831440.aspx
I tried to test this, but switching from “Server with a GUI” to Server Core removes the Application Identity service, which is required for enforcement of AppLocker rules. The AppLocker event log is also removed.
This was the second one I found:
In Windows Server 2012 and Windows 8
AppLocker is supported on all Windows beta evaluation versions except the Server Core installation option.
http://technet.microsoft.com/en-us/library/ee619725(v=ws.10).aspx
Mmm, it only mentions the “beta evaluation” version, so a strong hint, but no definitive statement.
In the end I received a response from someone within Micrsoft to a Technet Forum post. You can read the full thread here: