Agricultural Guest Worker Reform Initiative Act of 2019 or the AGRI Act of 2019 This bill revises provisions related to H-2A (temporary agricultural worker) visas, including to eliminate certain requirements to hire U.S. workers, expand the program to include dairy and ranch workers, and shift administrative responsibilities from the Department of Labor to the Department of Agriculture (USDA). The bill establishes a trust fund to be used to (1) administer and enforce the program, (2) collect a portion of guest worker wages to be paid upon a worker's return to the worker's country of origin, and (3) provide emergency medical services for guest workers. The bill eliminates a requirement that, during the first half of the time period of a guest worker contract, certain employers must hire any qualified U.S. employee who applies to perform the job the guest worker was hired to perform. Furthermore, an employer shall not be required to pay a guest worker a wage higher than the highest of federal, state, or local minimum wage rates. The bill places limitations on when guest workers may receive civil legal assistance for low-income individuals. Employer-provided housing shall be governed generally by USDA regulations, where currently such housing must meet applicable federal, state, or local standards. Employers shall not have to provide housing to workers who can reasonably return to their permanent residence within the same day. An employer may file a civil action to recover transportation costs from a guest worker who absconds from a contract.