We study the polarization of inclusive J/ψ produced in Pb-Pb collisions at sqrt[s_{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<4, for three transverse momentum intervals (2<4, 4<6, 6<10 GeV/c) and as a function of the centrality of the collision for 2<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/ψ 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 3.9σ at low p_{T} and for intermediate centrality values. The polarization could be connected with the behavior 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.
