I recently read Scott Chacon\'s post \"Smart HTTP Transport\", and I was hoping that it might have become possible via IIS (windows 7) since that post was written. I haven\'t be
You might be able to do this with the Rack support in IronRuby (http://github.com/jschementi/ironruby/tree/master/Merlin/Main/Hosts/IronRuby.Rack) and the Git http server rack app (http://github.com/schacon/grack). You need at least Git 1.6.6, possibly 1.7.0 for this to work - I'm not sure that it will, but it might. If you're running any Java app servers, you can compile Grack into a WAR, too, if that's an option.
I just created a project. It has an ASP.NET HttpHandler that follows what Grack does. Welcome to try it out.
GitAspx - By Jeremy Skinner
http://github.com/JeremySkinner/git-dot-aspx/downloads
Install Instructions
http://www.jeremyskinner.co.uk/2010/10/19/gitaspx-0-3-available/
Git Web
http://gitweb.codeplex.com/
Bonobo Git Server
http://www.chodounsky.net/bonobo-git-server/
WebGitNET
https://github.com/otac0n/WebGitNet
Alternatively ... (non-IIS)
Gitea (fork of Gogs): https://gitea.io
Gogs: https://gogs.io
SCM Manager allows you to easily setup Git, Hg, and SVN servers over HTTP/HTTPS under a separate Java process and complete with built in authentication.
http://www.scm-manager.org/
https://bitbucket.org/sdorra/scm-manager/