I wrote about (binary) data transfer by modem:
> At least as early as 1965 IBM sold equipment that
could do this,
John Allain wrote:
Some more date/a:
""the first model of the first commercial modem," a box in which a phone
handset could be placed, allowing a computer to say "beep beep" to
another over long distances. Lee was almost right. He actually had the
second model of the "magnetic/acoustic coupler," manufactured for
Tymshare, Inc. by Climet Instruments about 1966"
--
http://membres.inforoots.org/dguardiola/Lee_Felsenstein/CMP-mails.htm
The Bell 103A modem was introduced in 1962. I suspect that it was the
first commercial modem.
The date that's harder to place is when the 103A was first used for
computer-to-computer data transfer, as opposed to teletype-to-teletype
or teletype-to-computer communication.