  Aims. The optical emission of black hole transients increases by several
magnitudes during the X-ray outbursts. Whether the extra light arises from the
X-ray heated outer disc, from the inner hot accretion flow, or from the jet is
currently debated. Optical polarisation measurements are able to distinguish
the relative contributions of these components. Methods. We present the results
of BVR polarisation measurements of the black hole X-ray binary MAXI J1820+070
during the period of March-April 2018. Results. We detect small, $\sim$0.7%,
but statistically significant polarisation, part of which is of interstellar
origin. Depending on the interstellar polarisation estimate, the intrinsic
polarisation degree of the source is between $\sim$0.3% and 0.7%, and the
polarisation position angle is between $\sim10\deg-30\deg$. We show that the
polarisation increases after MJD 58222 (2018 April 14). The change is of the
order of 0.1% and is most pronounced in the R band. The change of the source
Stokes parameters occurs simultaneously with the drop of the observed V-band
flux and a slow softening of the X-ray spectrum. The Stokes vectors of
intrinsic polarisation before and after the drop are parallel, at least in the
V and R filters. Conclusions. We suggest that the increased polarisation is due
to the decreasing contribution of the non-polarized component, which we
associate with the the hot flow or jet emission. The low polarisation can
result from the tangled geometry of the magnetic field or from the Faraday
rotation in the dense, ionised, and magnetised medium close to the black hole.
The polarized optical emission is likely produced by the irradiated disc or by
scattering of its radiation in the optically thin outflow.
