No of course not, Microsoft have no reason to provide ASP.Net for Nginx.
If you are using Windows, then use IIS (or if you must Apache). On Windows, Nginx is very ropey, to quote the manual:
Version of nginx for Windows uses the native Win32 API (not the Cygwin
emulation layer). Only the select() connection processing method is
currently used, so high performance and scalability should not be
expected. Due to this and some other known issues version of nginx for
Windows is considered to be a beta version.
Windows running Nginx/FastCGI/Mono, aside from an academic exercise to see if it's possible, is a terrible idea. If you philosophically don't want to use the Microsoft stack then do it properly and run Nginx/FastCGI/Mono on Linux - it's pretty simple to setup.