Microsoft has just added the ability to deploy directly to an Azure Website from a Git repository. All you have to do is place the following into your README.md file:
[![Deploy to Azure](http://azuredeploy.net/deploybutton.png)](https://azuredeploy.net/)
You can also use standard HTML tags to provide your own button like this:
<a href="https://azuredeploy.net/" target="_blank"> <img src="http://azuredeploy.net/deploybutton.png"/> </a>
The following video describes the process in more detail.