Dark matter may consist of axion-like particles with ultra-low masses. Two-photon interactions of these particles affect the polarization of radiation propagating through the dark matter. Coherent oscillations of the Bose condensate of the particles induce periodic changes in the plane of polarisation of emission passing through the condensate. We estimate this effect and analyze MOJAVE VLBA polarization observations of bright downstream features in the parsec-scale jets of active galaxies. Through the non-observation of periodic changes in the polarization angle, we are able to constrain the photon coupling of the ultra-light dark-matter axion-like particles at the level of less than or similar to 10(-12) GeV-1 for masses between similar to 5 x 10(-23) eV and similar to 1.2 x 10(-21) eV.