The Cadmium Zinc Telluride Imager (CZTI) on board AstroSat has been regularly detecting gamma-ray bursts (GRBs) since its launch in 2015. Its sensitivity to polarization measurements at energies above 100 keV allows CZTI to attempt spectropolarimetric studies of GRBs. Here, we present the first catalog of GRB polarization measurements made by CZTI during its first five years of operation. This includes the time-integrated polarization measurements of the prompt emission of 20 GRBs in the energy range 100-600 keV. The sample includes the bright GRBs that were detected within an angle range of 0 degrees-60 degrees and 120 degrees-180 degrees where the instrument has useful polarization sensitivity and is less prone to systematics. We implement a few new modifications in the analysis to enhance the polarimetric sensitivity of the instrument. The majority of the GRBs in the sample are found to possess less/null polarization across the total bursts' duration in contrast to a small fraction of five GRBs that exhibit high polarization. The low polarization across the bursts might be due either to the burst being intrinsically weakly polarized or to a varying polarization angle within the burst even when it is highly polarized. In comparison to POLAR measurements, CZTI has detected a larger number of cases with high polarization. This may be a consequence of the higher energy window of CZTI observations, which results in the sampling of a shorter duration of burst emissions than POLAR, thereby probing emissions with less temporal variation in polarization properties.