Microwave-induced zero-resistance states appear when the associated B-1-periodic magnetoresistance oscillations grow in amplitude and become comparable to the dark resistance of the two-dimensional electron system (2DES). Existing theories have made differing predictions regarding the influence of the microwave polarization in this phenomenon. We have investigated the effect of rotating, in-situ, the polarization of linearly polarized microwaves relative to long-axis of Hall bars. The results indicate that the amplitude of the magnetoresistance oscillations is remarkably responsive to the relative orientation between the linearly polarized microwave electric field and the current-axis in the specimen. At low microwave power, P, experiments indicate a strong sinusoidal variation in the diagonal resistance Rxx vs. θ at the oscillatory extrema of the microwave-induced magnetoresistance oscillations. Interestingly, the phase shift θ0 for maximal oscillatory Rxx response under photoexcitation is a strong function of the magnetic field, the extremum in question, and the magnetic field orientation.