New to Azure, I'm looking for a good way of deploying our apps. The situation is that we build our Java apps inside our network using Jenkins. Each successful build should be automatically published to the production environment on Azure. We cannot have any port opened from our network to Azure other than https. To make it even worse, we need to go through an http/s proxy. Note that we can only deploy compiled war-files. No code is allowed to be published outside our network.
What would be the options in our case?
Your issue isn't really the WAR file, that's pretty easy to deal with. Once you setup an Azure web app to run Java if you drop the WAR in the root of an Azure web app then it will get loaded and deployed.
The issue your going to have is getting it up to Azure with only outbound https allowed. You can't use any of the deployment mechanisms built into Azure Web Apps as they don't run on port 443.
The only thing I could think of would be to have your build process upload the file to Azure storage, which does use outbound 443. Then you could create an Azure automation Powershell job that takes the file from storage and publishes to the web app using web deploy or ftp or similar. You could have your build process trigger this by setting up your automation job with a webhook, which you can hit from your build server as it's running on 443.