Aperture synthesis is a powerful technique for imaging the radio sky and can be used to make images in all four Stokes parameters, providing a complete measurement of the polarization state of the received radiation. In centimeter-wavelength continuum astronomy the received signals are generally partially linearly polarized, with a negligibly small fraction of circular polarization. For this application the preferred antenna configuration receives both left- and right-hand circular polarization. In this paper the effects of nonideal antenna performance are analyzed, and calibration and data correction procedures are described which allow precise measurement of the four Stokes parameters. Three levels of data correction are identified. Level 1, complex channel gain correction, is the standard calibration of amplitude and gain required in every synthesis telescope. Level 2, orthogonality correction, makes the instrument appear as a set of interferometers, identical to the level of approximation involved, which have two orthogonal, but not precisely circular, polarizations. Level 3 correction converts the telescope into an array of identical antennas with exactly circular polarization. Level 3 correction gives the most accurate polarimetry; for this level of correction the polarization characteristics of one antenna, which is used as a reference, must be determined. In the absence of a precise determination of the polarization characteristics of the reference antenna, a measurement which may be very difficult, there is no value in proceeding to Level 3 correction. If the cross-hand contamination of the antennas is less than about 15%, then only level 1 and level 2 corrections are needed to achieve a sensitivity to polarized emission of 1% of the total intensity, an accuracy of measurement of polarized intensity of better than 10% and a measurement of the position angle of linearly polarized emission better than 5°. The implementation of polarimetry at 1420 MHz on the Dominion Radio Astrophysical Observatory synthesis telescope, Penticton, British Columbia, Canada, is described, and instrument performance to the above specifications is demonstrated. Observations of the supernova remnant DA530 are presented, demonstrating a usable field of view for polarimetry of at least 1.5°.