The Jet Configuration Service (JCS) is capable of being installed on a wide variety of database and Operating systems - including SQL Server 2012 and 2012 R2.
Azure SQL - while similar to SQL Server 2012 - is not identical to SQL Server 2012 and is not directly compatible with all version of the installer for the JCS.
However, it is still possible for an Azure administrator to configure the Azure portal to be able to install the JCS.
The JSC installation sets are included with both Jet Essentials and Jet Enteprise.
Starting in March of 2014, those JCS installation sets which requiring special Azure configuration steps contain specific instructions for installing on Azure.
Please refer to the READ_ME_FIRST.TXT file located in the "JCS Azure configuration files" folder for instructions on configuring the Azure portal.