There is a AX 2012 virtual machine available on the Azure Portal.  When I tried to create one, I received the following error (with typo):

Project was created but there were problems creating deployment instance. You need to be a service administrator or co-administator for the selected Azure subscription or the location selected may not be supported for deploying Microsoft Dynamics AX 2012 R3 instances.

This happens because Azure environment does not trust Lifecycle Services.

  1. Open Lifecycle services to the project you tried to use
  2. Go to Microsoft Azure settings
  3. Download the management certificate
  4. Open the old Azure Management portal.
  5. Go to Settings > Management Certificates
  6. Upload the certificate.
  7. Go back to Lifecycle services and click the plus sign to create an environment and follow the steps.