I added both SMS & voicemail messaging to one of my commercial apps for schools several years ago. It works well.
To do so, you will need a suitable provider who will have an API for you to use - I used Twilio as their prices were reasonable and their documentation is excellent. Files can be in various formats: CSV, XML or JSON. Each has advantages and disadvantages
I have written many posts about this at various forums including this lengthy thread whilst I was developing the code:
Using-twilio-with-access-to-send-receive-text-voice-messages
I strongly recommend you read this article which was enough to get me started:
Twilio-from-excel-and-access
Although I'm very happy with my chosen provider, there are several other providers to choose from so do some research yourself.
Good luck