We present a detailed statistical analysis of the alignment of polarizations of radio sources at high redshift. This study is motivated by the puzzling signal of alignment of polarizations from distant quasars at optical frequencies. We use a coordinate invariant measure of dispersion to test for alignment of polarizations of widely separated sources. The data from JVAS/CLASS 8.4 GHz surveys are used for our study. We find that the data set with polarization flux greater than 1 mJy shows a significant signal of alignment at distance scales of order 150 Mpc. The significance of alignment decreases as we go to larger distances. In contrast the data set with polarization flux less than 1 mJy does not show significant alignment at short distances. However this set, as well as the full data sample, shows a very significant signal at large distances of order 500–850 Mpc. Due to the presence of relatively large error in the low polarization sample, this signal needs to be tested further with more refined data. We also study the signal by imposing a cut on the error in polarization. We find that the significance of alignment increases with decrease in fractional error. We are unable to attribute our results to known sources of bias. We discuss a possible physical explanation of our results.