it is possible, but you will need to get additional libraries and access to an SMS service to actually send the messages over the phone network (or, far more expensive unless you do it a LOT, get the hardware to do it yourself).
I've never done it myself but I've done some limited research into the options and that's what it turned up. At the time it was decided that all options were more expensive than the expected ROI so the project wasn't continued past the initial feasibility study.
You can go two ways. One is to hire the services of a 3rd party to send the messages for you. In that case you typically need no hardware, just an API and an internet connection to them (they may supply the API or give you specifications it should conform to).
The other is to interface directly with the mobile phone network. This will need hardware, the network providers should have information about this. This is the more expensive route unless you send a LOT of messages (there is usually a cost to sending messages through a 3rd party distributor in addition to a subscription fee).