It looks like System.Net.WebSockets namespace is already available on Xamarin.
This said, we actually wrote a simple multiplatform WebSocket library that uses TLS/SSL and HTTP API provided by Rebex.Networking assembly. We are considering whether to release it to the public.
Our intention was to target .NET 4.0 on Windows 7 or earlier (where System.Net.WebSockets is not implemented) and also legacy platforms such as .NET 2.0/3.0/3.5 and .NET Compact Framework 2.0/3/5/3.9. Adding support for Xamarin platforms would be very simple.
So if you can't use System.Net.WebSockets on Xamarin platforms for some reason, please let us know.