The measurement of J/ψ azimuthal anisotropy is presented as a function of transverse momentum for different centralities in Au+Au collisions at sqrt[s(NN)]=200 GeV. The measured J/ψ elliptic flow is consistent with zero within errors for transverse momentum between 2 and 10 GeV/c. Our measurement suggests that J/ψ particles with relatively large transverse momenta are not dominantly produced by coalescence from thermalized charm quarks, when comparing to model calculations.