In the 1950s, ROC curves were employed in psychophysics to assess human (and occasionally non-human animal) detection of weak signals.
Green and Swets (1966) is cited as attesting to that fact. I don't have any way of accessing that book, and nor would it necessarily constitute the first proposal of ROC curves for usage in psychology.
Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. Society, 1, 521.