NASAs Small Explorer Mission GEMS (Gravity and Extreme Magnetism SMEX), scheduled for launch in 2014, will have the sensitivity to detect and measure the linear polarization properties of the 0.5 keV and 2-10 keV X-ray emission of a considerable number of galactic and extragalactic sources. The prospect of sensitive X-ray polarimetry justifies a closer look at the polarization properties of the basic emission mechanisms. In this paper, we present analytical and numerical calculations of the linear polarization properties of inverse Compton scattered radiation. We describe a generally applicable formalism that can be used to numerically compute the polarization properties in the Thomson and Klein-Nishina regimes. We use the code to perform for the first time a detailed comparison of numerical results and the earlier analytical results derived by Bonometto et al. (1970) for scatterings in the Thomson regime. Furthermore, we use the numerical formalism to scrutinize the polarization properties of synchrotron self-Compton emission, and of inverse Compton radiation emitted in the Klein-Nishina regime. We conclude with a discussion of the scientific potential of future GEMS observations of blazars. The GEMS mission will be able to confirm the synchrotron origin of the low-energy emission component from high frequency peaked BL Lac objects. Furthermore, the observations have the potential to decide between a synchrotron self-Compton and external-Compton origin of the high-energy emission component from flat spectrum radio quasars and low frequency peaked BL Lac objects.
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