A new distinct variety of grapevine named ‘ARRATWENTYNINE’ abundantly forms attractive large firm and meaty seedless berries with a red skin coloration in medium-large clusters which display a sweet apple flavor. The fruit commonly is ready for harvesting during June in 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.