It's not easy to be absolutely sure but I think the first use of a similar term was by Jack Binder. He coined the term zero-gravity in an article published in "Thrilling Wonder Stories" in 1938, but it referred to the absence of apparent gravity at the center of the Earth.

I think the first modern use of zero-g was in the 1952 novel "Islands in the Sky" by the late, great Arthur C. Clarke. But someone could have use the term earlier and I just don't know about it.