Healthcare Worker Retention Act This bill establishes through 2024 a new refundable health care worker tax credit, equal to $1,000 for individual taxpayers (1) who work in a healthcare setting as an employee or contractor for at least an average of 20 hours per week, and 3 months during each half of a taxable year; and (2) whose gross income does not exceed $100,000 ($200,000 for joint returns or for a surviving spouse). The bill defines healthcare setting as an organization that provides healthcare services in specified settings, including a hospital, a nursing home, a community-based healthcare center, a school or college campus, a primary care facility, an assisted living facility, a hospice or home care, emergency medical services, or any other licensed facility that extends healthcare services to patients, including the elderly and disabled. The bill directs the Internal Revenue Service to establish a program to make semiannual advance payments of healthcare worker tax credit amounts.