A new distinct variety of grapevine named ‘ARRATHIRTYTWO’ abundantly forms attractive large firm seedless berries with an attractive black skin coloration in medium-to-large clusters which display a naturally sweet flavor. The fruit commonly is ready for harvesting during August in the San Joaquin Valley of Central California, U.S.A, and displays good eating qualities as a table grape. The fruit firmness renders the fruit well amenable for handling, shipping, and storage.