Hello,
I am not quite sure, if the following method works for you. However, I am suggesting to try this option.
You may create Container based Azure Web for this page: https://portal.azure.com/#create/Microsoft.WebSite
(Also refer my blog: http://cloudcompute.info/publish-docker-images-from-container-registry-in-azure-app/)
Once you have this ready with your container application, you can assign a custom domain for the application. This custom domain will have a static IP from your provider (Go Daddy etc.)
Following reference from my blog helps on this step
http://cloudcompute.info/how-to-configure-an-azure-app-from-marketplace-in-a-custom-domain/
Please mark as "Accept the answer" if the above steps helps you. Others with similar issues can also follow the solution as per your suggestion
Regards,
Manu