Azure Web App Port Mapping/Forwarding

Is it possible to map or forward an external port x to port 80 in a Web App on Azure with any of the tools provides by Azure (e. g. Traffic Manager etc.). I'm not talking about VMs, I'm talking about the more abstract App Service.

Given is the following example:

We run a windows service on many devices which connect to an API on Port 314XX. We now run this Asp.Net Web Api on Azure in a Web App, which is fine, but it is not possible to update all devices, so some of them will still be connecting to port 314XX instead of 80. Is it possible to configure a Web App in Azure to listen on multiple port or is it possible to use any of these traffic tools to create such a port mapping? As of today, I haven't found any way to do this.

Thanks for your help.

Unlike Cloud Services (web/worker roles) and Virtual Machines, Web Apps don't have a port-mapping feature. That is... the only ports open for Web Apps are 80 and 443.

Traffic Manager does not provide port-mapping. You'd need to run your own proxy for handling this.