What you need is an SMS gateway that will let you send out text messages via an API. A quick Google search yields Zeep Mobile, which lets developers send SMS text messages for free from their application.
Because it's free, there may very well be some restrictions, but if you architect your app correctly using a strategy or adapter pattern then you should be able to replace this module later on down the road with something more advanced based on the needs of your application.
The primary restriction on the free plan is that it's ad-supported. This may very well be ok for you during initial development and testing, but your production users will likely find this to be a significant problem in using your service. Zeep does have a paid plan that eliminates the ads, and there are of course countless other SMS gateways that have API's that you can use for a fee.