  The polarization of quarkonium states produced in hadron collisions exhibits
strong non-perturbative effects - for example, at small transverse momentum
$p_t$ charmonia appear unpolarized, in sharp contradiction to the predictions
of perturbation theory. The quark--gluon plasma is expected to screen away the
non-perturbative physics; therefore those quarkonia which escape from the
plasma should possess polarization as predicted by perturbative QCD. We
estimate the expected $J/\psi$ polarization at small $p_t$, and find that it
translates into the asymmetry of the $e^+e^- (\mu^+\mu^-)$ angular distribution
$W(\theta) \sim 1 + \alpha cos^2\theta$, with $\alpha \simeq 0.35 \div 0.4$.
