We report on the first measurement of inclusive J/ψ elliptic flow v2 in heavy-ion collisions at the LHC. The measurement is performed with the ALICE detector in Pb-Pb collisions at √(s(NN))=2.76 TeV in the rapidity range 2.5<y<4.0. The dependence of the J/ψ v2 on the collision centrality and on the J/ψ transverse momentum is studied in the range 0≤p(T)<10 GeV/c. For semicentral Pb-Pb collisions at √(s(NN))=2.76 TeV, an indication of nonzero v2 is observed with a largest measured value of v2=0.116±0.046(stat)±0.029(syst) for J/ψ in the transverse momentum range 2≤p(T)<4 GeV/c. The elliptic flow measurement complements the previously reported ALICE results on the inclusive J/ψ nuclear modification factor and favors the scenario of a significant fraction of J/ψ production from charm quarks in a deconfined partonic phase.