Messagebird provides a API you could try. You can test this API via a REST Call. I have good experience with this, well documented and perfect uptime.
there is a whole set of module is the marketplace which will help you to implement such
Didn’t use them myself yet, though I expect that when you know how to model a Mx app, these will be sufficient
In addition to the other answers, if you are just looking to send a message from a mobile device that is running your application, you can use the “Send Text Message” activity in Nanoflow Commons.