The CARMA 1.3 mm polarization system consists of dual-polarization receivers that are sensitive to right- (R) and left-circular (L) polarization, and a spectral-line correlator that measures all four cross polarizations (RR, LL, LR, RL) on each of the 105 baselines connecting the 15 telescopes. Each receiver comprises a single feed horn, a waveguide circular polarizer, an orthomode transducer (OMT), two heterodyne mixers, and two low-noise amplifiers (LNAs), all mounted in a cryogenically cooled dewar. Here we review the basics of polarization observations, describe the construction and performance of key receiver components (circular polarizer, OMT, and mixers -- but not the correlator), and discuss in detail the calibration of the system, particularly the calibration of the R-L phase offsets and the polarization leakage corrections. The absolute accuracy of polarization position angle measurements was checked by mapping the radial polarization pattern across the disk of Mars. Transferring the Mars calibration to the well known polarization calibrator 3C286, we find a polarization position angle of $chi = 39.2 pm 1^{circ}$ for 3C286 at 225 GHz, consistent with other observations at millimeter wavelengths. Finally, we consider what limitations in accuracy are expected due to the signal-to-noise ratio, dynamic range, and primary beam polarization.
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