While any of several SMS service providers should do the trick, it's worth nothing that Digital Ocean posted a guest blog post for Twilio a while back, talking about how Twilio and Digital Ocean play well with each other: https://www.twilio.com/blog/2014/10/digitalocean-communicates-clearly-with-twilio-sms-nt.html
Personally I've had good experiences with using IFTTT's "Maker Webhooks" plugin. It allows me to send a curl command (in good old command-line Bash) from a droplet to maker.ifttt.com to trigger a generic IFTTT "event". The event can then be translated into sending an SMS message, or sending an email, or turning on a Philips Hue light, or an LED or my Raspberry Pi, or whatever.
I haven't used Twilio in several years, but back then at least the experience was also quite good. It costs money, but not much, and seemed very reliable and easy to use.
Use the online SMS gateway to make all your business communications lighting fast and more efficient. Out gateway is specifically designed for all types of marketing and business alerts campaigns. It allows users to pre-schedule and send out hundreds of promotional SMS or meeting and event reminder instantly, all over the globe.
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