From wiki:
ARINC
In 1978 ARINC introduced ACARS© (Aircraft Communications Addressing and Reporting System), which is a datalink system that enables ground stations (airports, aircraft maintenance bases, etc.) and commercial aircraft to communicate without voice, but data, due to the datalink system being integrated with aircraft systems via a Communications Management Unit (CMU), such as fuel quantity, weight on wheels, FMS, etc.
I doubt that an acronym would have an acronym as one of its elements (i.e. it wouldn't be ACARS, if the A stood for AIRINC, it would be AIRINCARS)