Web Roles as well as Worker Roles are available on Windows Azure Cloud Services.
Windows Azure Website do not have Worker Roles.
However, you can have Windows Azure Website talking to your Worker Roles via Bus Services.
I hope I don't have to rebuild my entire project as a cloud project ...
I do not know how your application looks like, but Web Roles are very similar to web applications, so maybe it would be worth investigating potential change from "standard" web application to Azure Web Role.
Azure Web Roles provide lots of advantages like roles scalability, code deployment management etc.
Update: Azure Websites now support SSL for custom domain, for more information check the ScottGu's link about the announcement.
Update: Azure Websites now support scaling too.
Also bear in mind that currently Azure Web Sites do not support SSL for custom domains which could be a blocker for your application move to the cloud.