Yon want to use your local Windows Active Directory as an identity
provider to Windows Azure, I think you're looking for a SSO solution, it
can be archived with the Access Control Service or Windows Azure Active
About these two service, please read: Azure Active Directory is the future of ACS.
This blog provides a video on how to do it with ACS.
This post: Windows
Azure ACS with Active Directory as identity provider for SSO, also
should be helpful.