It's a work in progress. You can do it right now but it's more steps than we would like to.
For example, about a month ago you had to publish a python interpreter, site packages, wfastcgi handler and your web app, then configure environment variables and the handler in the azure web site configuration page.
Since then we've been able to simplify it by having Python 2.7 and wfastcgi (any day now) pre-installed on the system that hosts the web site. You now just have to publish your site-packages and your web app (then do the configuration). An immediate
benefit of that, besides being simpler, is that someone can now develop an azure web site without having a Windows Python 2.7 interpreter (that helps people developing from Linux or Mac).
Ideally, you'd pick your favorite web framework from a drop down box from the azure portal, and azure would install that framework and do the configuration for you. Hopefully we'll get there soon.
As of now, you should be able to use frameworks other than Django. The wfastcgi handler is flexible enough, you just need to set up the WSGI_HANDLER environment variable correctly.
Thanks for you interest!