As "SMS provider" would not have any value without the SMS-enabled communication networks behind it, you should really look at "
SMS gateway":
http://en.wikipedia.org/wiki/SMS_gateway[
^].
Normally, they serve for some fee, but some do it for free. You need to perform your own search, as I don't think we can promote any proprietary 3rd-party services here, even free-of-charge ones.
—SA