Deploying to App Service from Jenkins is made easy with the App Service plugin. If you already have a Jenkins server, follow these instructions to get started with the plugin.
If you do not already have a Jenkins server, you can create one from the Azure Marketplace. Once your Jenkins server is up and running, follow the previous link to configure the App Service plugin.
To use the Jenkins plugin for App Service, you will need to create a service principal (also known as an App Registration) with Contributor rights. The Jenkins plugin will use this principal to authenticate with Azure and deploy your Java app to App Service.