This question was answered in this but there is no explanation on how they did it? Is there any step by step method on how can I upload a webservice into wordpress site?
Is it Possible to upload a ASP.Net WebService
Yes It is possible WebService can be hosted. your question should be how can we do that rather than this. A simple answer to that is contact your Host. One needs an IIS server to host stuff that is build in .NET Framework specifically if that is a WebService API or any thing that requires HTTP Protocol.
After Hosting a webservice your question will/Should be how to access it, that is a totally different question and you can find help related to that Here and Here
I hope this helps you in any way and don't worry about vote down you'll get used to