This post shows you how to setup RDS 2012 on Windows Azure: please see previous posts for guides on configuring RDS.
Deploy RDS VM
Ensure you setup the Virtual Network and Domain controller before deploying the RDS VM. You can ether create a site to site VPN to a on-premise Domain Controller or create a new domain on Azure.
To create the RDS Virtual machine, navigate to the Virtual Machines tab and select New at the bottom left of the screen.
Create a VM from the from gallery and follow the instructions.
Once the VM is provisioned, you will need to remote to the server, configure basic settings, join the domain and deploy the services.
Configuring Endpoints for Web Access
To enable web services on the public domain you would need to create a endpoint allowing TCP 443.
Select the Virtual Machines tab and then select the RDS server. You will then be presented with a Dashboard screen, select Endpoints.
Add the port TCP 443 for web access.
Once configured you will be able to access the RDS Web page and access resources using https://Servername.cloudapp.net/rdweb . You can configure DNS servers with a CNAME to point the server to a domain of your choice.
Ryan Mangan's IT Blog 
Interesting post, but… there is currently no licensing model that allows RDS on Azure or any other public cloud. So RDS can not be run on Azure.
Hi, thanks for your post.
As you can see from my post you can deploy RDS on Azure, but at present there is no licensing model for this moment in time. Please see the post http://oakleafblog.blogspot.com.es/2012/06/installing-remote-desktop-services-on.html for further information.
This deployment is great for testing and to show Azures capabilities.
Best Regards,
Just to keep things updated, this is now supported. Thanks Ryan.