  Predictions are made for elliptic flow in collisions of polarized deuterons
with a heavy nucleus. It is shown that the eccentricity of the initial
fireball, evaluated with respect to the deuteron polarization axis
perpendicular to the beam direction, has a substantial magnitude for collisions
of highest multiplicity. Within the Glauber approach we obtain $\sim 7\%$ for
the deuteron states with spin projection 0, and $\sim -3 \%$ for spin
projection $\pm 1$. We propose to measure the elliptic flow coefficient as the
second order harmonic coefficient in the azimuthal distribution of produced
charged hadrons with respect to the fixed polarization axis. Collective
expansion yields a value of the order of $1\%$ for this quantity, as compared
to zero in the absence of polarization and/or collectivity. Such a vivid
rotational symmetry breaking could be measured with the current experimental
accuracy of the relativistic heavy-ion experiments. The effect has a
fundamental significance for understanding the nature of dynamics in small
systems, as its experimental confirmation would prove the presence of the
shape-flow transmutation mechanism, typical of hydrodynamic expansion or
rescattering in the later stages of the fireball evolution.
