The polarization properties of radio sources powered by an Active Galactic Nucleus (AGN) have attracted considerable attention because of the significance of magnetic fields in the physics of these sources, their use as probes of plasma along the line of sight, and as a possible contaminant of polarization measurements of the cosmic microwave background. For each of these applications, a better understanding of the statistics of polarization in relation to source characteristics is crucial. In this paper, we derive the median fractional polarization, $Pi_{0, rm med}$, of large samples of radio sources with 1.4 GHz flux density $6.6 < S_{1.4} < 70$ mJy, by stacking 1.4 GHz NVSS polarized intensity as a function of angular size derived from the FIRST survey. Five samples with deconvolved mean angular size 1.8 to 8.2 and two samples of symmetric double sources are analyzed. These samples represent most sources smaller than or near the median angular size of the mJy radio source population We find that the median fractional polarization $Pi_{0,rm med}$ at 1.4 GHz is a strong function of source angular size less than ~5 and a weak function of angular size for larger sources up to ~8. We interpret our results as depolarization inside the AGN host galaxy and its circumgalactic medium. The curvature of the low-frequency radio spectrum is found to anti-correlate with $Pi_{0,rm med}$, a further sign that depolarization is related to the source.
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