Received (to be inserted by publisher); Revised (to be inserted by publisher); Accepted (to be inserted by publisher); X-ray polarimetry promises to give qualitatively new information about high-energy astrophysical sources, such as binary black hole systems, micro-quasars, active galactic nuclei, neutron stars, and gamma-ray bursts. We designed, built and tested a X-ray polarimeter, X-Calibur, to be used in the focal plane of the balloon-borne InFOCµS grazing incidence X-ray telescope. X-Calibur combines a low-Z scatterer with a CZT detector assembly to measure the polarization of 20 − 80 keV X-rays making use of the fact that polarized photons scatter preferentially perpendicular to the electric field orientation. X-Calibur achieves a high detection efficiency of 80%. The X-Calibur detector assembly is completed, tested, and fully calibrated. The response to a polarized X-ray beam was measured successfully at the Cornell High Energy Synchrotron Source. This paper describes the design, calibration and performance of the X-Calibur polarimeter. In principle, a similar space-borne scattering polarimeter could operate over the broader 2 − 100 keV energy band.