Looking through the Azure Reference I can't find any references to the REST API (or any API) for Azure App Services, Service Plans, Web apps etc
Is there a REST API for Azure App Services?
I have seen Are there no Rest Api for deploying Azure Websites? But there have been a huge number of changes to Azure since 2013.
UPDATE - 01-Mar-2017
The answer below is obsolete as when the answer was provided the REST API was not documented. It is now :). The REST API documentation is available here: https://docs.microsoft.com/en-us/rest/api/appservice/.
I'm sure that there's a REST API. It's just that it is not documented yet. Whenever I need to find REST API for something that has not been documented, one thing I normally do is run
Azure PowerShell Cmdlets in debug mode. It tells me all the information I need (though I must say that it is not a substitute for documentation).