Controlling a Relay via Cellular Data Only, no SMS or Calls

I have an situation where I want to be able to remotely switch on and off a relay via cellular connection. The catch is that the sim card for this application doesn’t accept voice calls or SMS, it only does data. There are so many articles about controlling things via SMS that I haven’t been able to find any yet that use some other method. Can anyone point me in the right direction?

For this application AC power is abundant and cell service is good, though I’d like to keep the data usage minimized. I’d like to use Arduino but if it turns out to not be possible, a pi is also an option.