Deploying a project that uses the Telerik® UI for ASP.NET AJAX to Windows Azure is not very different than deploying a standard application. More information can be found in the following resources:
WebResource requests are not returned, which results in missing CSS files and/or scripts.
This can often seem like an intermittent problem - i.e. after some deployment attempts the Telerik controls will work, after some - they will not.
The reason behind this behavior, however, is within Microsoft's servers - when you upload from a location that is ahead of the time zone in which the Azure servers are located the AssemblyResourceLocator does not work correctly until the servers catch up to the local time in which you upload. This is explained in this thread in Microsoft's forums.
This means that usually simply waiting will resolve the situation. More information and an alternative approach is shown in Simon Holman's blog post Telerik CSS issues with Windows Azure.