We assume the answer is no. However, all SO questions are either dated or based on desktop browsers.
We're aware of WebRTC, but it's not supported in Mobile Safari today. Is there any other approach?
To clarify the scenario, imagine we had a service like Skype. Instead of requiring both parties to have the app, we would like one side to use a mobile browser to have phone calls.
No, you cannot. Not without plugins. If you want to place calls from a browser to any other client, you must use WebRTC for full support (media transport + media devices access) or you have to use a plugin to access the media devices and to do the transport (e.g. Flash).
As Mobile Safari still don't have WebRTC...