Agricultural Worker Program Act of 2019 This bill establishes a program for alien agricultural workers to obtain temporary resident status ("blue card status") and procedures to obtain permanent resident status. An alien shall qualify for the status if he or she performed the required amount of qualified agricultural work. The Department of Homeland Security may grant blue card status to qualified individuals who pass security checks and are not disqualified for various reasons, such as an aggravated felony conviction. DHS may waive certain disqualifications for humanitarian or public interest reasons. Blue card holders shall be authorized for employment in the United States and travel outside the United States. Such individuals shall be ineligible for various federal benefits, including the healthcare premium assistance tax credit. Individuals going through deportation or removal proceedings shall be given a chance to apply for blue card status if they qualify. Blue card holders may apply for permanent resident status, subject to various requirements, including work requirements over a specified time period and payment of federal taxes. Blue card status shall not last longer than eight years.