You're question is throwing lots of people off. You probably should have asked the question, "How do I send an SMS (Text) message from my C# app without paying for a third party vendor." Many people get caught up here on the details about having to use an API to do anything.
Depending on what you're trying to accomplish, I have a relatively simple answer for you. You'll have to do your own research [Google Searching], but I'm sure you can do it.
You can send SMS messages via Email messages. Email To Send SMS Messages
You will have to know the phone number of the person you want to text along with the carrier they are using for this method, but it does work. Try it out on your own phone with your email account.