Context. A number of works have reported that the polarization plane of extragalactic sources as well as the structural axes of radio sources are aligned on the large scale. However, both the claims and their interpretation remain controversial. Aims. For the first time, we explore the alignment of parsec-scale jets. Additionally, we use archival polarimetric data at different wavelengths in order to compare the relative orientations of the jets and the polarization planes of their emission. Methods. Using the flux density distribution in very long baseline interferometry radio maps from the Astrogeo database, we determine the parsec-scale jet orientation for the largest sample of active galactic nuclei to date. Employing the method of parallel transport and a sample statistics characterizing the jet orientation dispersion among neighbors, we test whether the identified jets are significantly aligned. Results. We show that the parsec-scale jets in our sample do not demonstrate any significant global alignments. Moreover, the jet direction is found to be weakly correlated with the direction of the polarization plane at different frequencies.