The dll
is missing in the published (deployed environment). That is the reason why it is working in the local i.e. Visual Studio but not in the Azure Website Environment.
Just do Copy Local = true
in the properties for the assembly(System.Web.Http.WebHost) and then do a redeploy, it should work fine.
If you get the similar error i.e. some other assembly missing, then make that assembly to copylocal=true and redeploy, repeat this iteratively - if you are unsure of its dependencies.