I couldn't find anywhere the answer that can we deploy Commerce site to Azure. Only documentation about CMS deployment to Azure is available and many times says that you have to make sure that other modules support Azure.
So does Commerce support Azure deployment?
Not the current version, since it requires SQL Server Full Text search. They have plans to support Azure in the next version.
Hope this helps.
Thanks Fredrik. Forgot that requirement (would have been able to connect the dots myself :D).
I'm happy when David notify this: http://world.episerver.com/Articles/Items/Commerce-with-cloud-support/
This seems to answer your question.