  Ultra-light dark matter may consist of axion-like particles with masses below
10^(-19) eV. 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 polarization changes, we are able to constrain the
photon coupling of the ultra-light dark-matter axion-like particles at the
level of <~ 10^(-12)/GeV for masses between ~5*10^(-23) eV and ~1.2*10^(-21)
eV.
