Marc Brettler and I had an exchange about this question a few years ago. Basically the term ANaKH or TaNaKH was invented and diffused by the Masoretes who flourished between the 6th and 10th centuries. During prior centuries Rabbinic literature did not have a term equivalent to the later Protestant concept of the Bible or the Christian formulation of the Old Testament. Now Jews treat
Thanks to all who have replied, including privately.
What I was really curious about is not merely when the term was invented, but also when and how it became used so commonly.
on the use of the term תנ"ך:
Tal Ilan, "The term and concept of TaNaKh." in What is Bible? (2012) 219-234
Hope that is helpful!
American Jewish University