I definitely recall seeing it around 1990. Was it around prior to that?
Online etymology dictionary’s earliest known entry in the english corpus is listed as 1985, and they suspect it originated in the early 1970s. For my money, when I rewrote the constitution for my university’s anime club I pulled our original articles of incorporation from 1983, and “anime” was used fairly frequently throughout.
The time frame sounds right. It was still called Japanimation back in 1983, when I first attended Lunacon. I may have heard “anime” about that time, but it wasn’t the common term.