You can't make a VoIP call with a pure ASP.NET application. The problem is HTTP is a stateless protocol that drops connections as soon as data transfer has occurred. VoIP is a real time application where you need to have a constant connection between the various parties (client-pbx-destination, usually).
As a result, you would need to extend your ASP.NET application with either a ClickOnce .NET Windows Forms Application or other component that runs a local application on the user's machine.