After choosing your Azure Web App trigger, you will need to connect your account. This is really easy and you only need one piece of extra information.
In the Azure portal go to your web app and click on the Settings button. Select the Properties option and copy the URL under DEPLOYMENT TRIGGER URL.
Then come back to Zapier and paste this URL to the Deployment URL textbox. Name your account. Your Azure Web App account will be tested for successful connection.
Azure has a feature called deployment slots, which are another site that is cloned from your existing one.
When you create an Azure action for your main site, the webhook is not called for deployment slot.
To fix this, you will need to create another account connection to Windows Azure Web Sites linked to you desired deployment slot as described above here.