  We study the polarization of inclusive J/$\psi$ produced in Pb$-$Pb
collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV at the LHC in the dimuon channel,
via the measurement of the angular distribution of its decay products. We
perform the study in the rapidity region $2.5<y<4$, for three transverse
momentum intervals ($2<p_{\rm T}<4$, $4<p_{\rm T}<6$, $6<p_{\rm T}<10$ GeV/$c$)
and as a function of the centrality of the collision for $2<p_{\rm T}<6$ GeV/c.
For the first time, the polarization is measured with respect to the event
plane of the collision, by considering the angle between the positive-charge
decay muon in the J/$\psi$ rest frame and the axis perpendicular to the
event-plane vector in the laboratory system. A small transverse polarization is
measured, with a significance reaching 3.9$\sigma$ at low $p_{\rm T}$ and for
intermediate centrality values. The polarization could be connected with the
behaviour of the quark$-$gluon plasma, formed in Pb$-$Pb collisions, as a
rotating fluid with large vorticity, as well as with the existence of a strong
magnetic field in the early stage of its formation.
