Motivated by the recent experiments with Rydberg atoms in an optical tweezer array, we accurately map out the ground-state phase diagram of the antiferromagnetic Ising model on a square lattice with longitudinal and transverse magnetic fields using the quantum Monte Carlo method. For a small but nonzero transverse field, the transition longitudinal field is found to stay nearly constant. By scrutinizing the phase diagram, we have uncovered a narrow region where the system exhibits reentrant transitions between the disordered and antiferromagnetic phases when the transverse field increases. Our phase diagram provides a useful benchmark for quantum simulation with the Rydberg-atom system.