With our latest UX deployment we introduced a new user experience to easily choose Docker images that are stored in an Azure Container Registry (ACR) repo. Moreover we offer you a single click continuous deployment experience using webhooks with the Preview SKUs of ACR.

For more information please check our intro doc at
https://aka.ms/webapp-linux, for more information about continuous deployment for containers check the following article
https://docs.microsoft.com/en-us/azure/app-service-web/app-service-linux-ci-cd