Feeding Our Rural Kids Act of 2023 or the FORK Act of 2023 This bill amends the Summer Food Service Program (SFSP) to establish a vehicle summer meal delivery pilot program. (The SFSP is a federally funded, state-administered program that reimburses providers that serve no-cost, healthy meals and snacks to children and teens at summer sites in low-income communities.) The Department of Agriculture (USDA) must award one-year grants of up to $100,000 for service institutions (e.g., school food authorities) to purchase or retrofit vehicles to facilitate the distribution of noncongregate meals as part of the SFSP. USDA must give priority to service institutions with high rates of students who are eligible for free or reduced-price lunches and that serve a high proportion of students from socially disadvantaged backgrounds. USDA must also ensure, to the maximum extent practicable, that service institutions receiving grants are located in diverse geographic areas.