You can try Twilio. It is free if you want to test, but after you have to pay.
They have a nice API with c# support.
// Download the twilio-csharp library from twilio.com/docs/csharp/install
using System;
using Twilio;
class Example
{
static void Main(string[] args)
{
// Find your Account Sid and Auth Token at twilio.com/user/account
string AccountSid = "AC3094732a3c49700934481addd5ce1659";
string AuthToken = "{{ auth_token }}";
var twilio = new TwilioRestClient(AccountSid, AuthToken);
var sms = twilio.SendSmsMessage("+15005550006", "+14108675309", "All in the game, yo", "");
Console.WriteLine(sms.Sid);
}
}