Asylum Seeker Work Authorization Act of 2019 This bill directs the Department of Homeland Security to provide employment authorization for eligible asylum applicants. Currently, such individuals are not entitled to employment authorization but may be granted such by the Department of Justice. Such employment authorization shall last for one year and be renewable for one-year terms during the period necessary to adjudicate the applicant's asylum claim. The bill also shortens the waiting period for receiving employment authorization to 30 days from the filing of the asylum application.