Here is simple example of Running Serivcestack with FSharp. Application hosted on heroku.
Reference for Servicestack you can found out on given link.
I mainly took two article as reference one is getting started with Servicestack with FSharp found here. It is by Sergey Tihon, on that site you can found many other article about functional programming and FSharp. A good way to start with FSharp and / or Functional Programming.
Another article I took help is here. In this article it is explained for NancyFx. Another wonderful framework for web development.
FSharp development is supported on Appharbor and also on Microsoft's windows Azure. But it is awesome to run on Linux / Heroku.
I personally wanted this because I don't want to choose one service / platform over other just because my development language is not supported but because of service, price, support etc they are providing. So, now I guess there is nothing like language constraint anywhere as a Dot Net developer. And I hope this help others too for choosing their deployment platform.