Polarization measurements in the X-ray and gamma-ray energy range can provide crucial information on massive compact objects such as black holes and neutron stars. The Polarized Gamma-ray Observer (PoGO) is a new balloon-borne instrument designed to measure polarization from astrophysical objects in the 30-100 keV range, under development by an international collaboration with members from United States, Japan, Sweden and France. To examine PoGO's capability, a beam test of a simplified prototype detector array was conducted at the Argonne National Laboratory Advanced Photon Source. The detector array consisted of seven plastic scintillators, and was irradiated by polarized photon beams at 60, 73, and 83 keV. The data showed a clear polarization signal, with a measured modulation factor of 0.42 ± 0.01. This was successfully reproduced at the 10% level by the computer simulation package Geant4 after modifications to its implementation of polarized Compton/Rayleigh scattering. Details of the beam test and the validation of the Geant4 simulations are presented.