The collective properties of final state hadrons produced in the high statistics _{44}^{96}Ru + _{44}^{96}Ru and _{40}^{96}Zr + _{40}^{96}Zr collisions at sqrt{s_textrm{NN}} = 200~textrm{GeV} are found to be significantly different. Such differences were argued to be precise probes of the difference in nucleon distribution in the isobar nuclei. We investigate the J/psi production in the isobar collision via a relativistic transport approach. By comparing the isobar systems according to equal centrality bin and equal multiplicity bin, we find that the yield ratio of J/psi is sensitive to the differences in both the number of binary collisions and the medium evolution. Besides, the elliptic flow v_2 of J/psi is qualitatively different from the light hadrons, and the ratio between Ru + Ru and Zr + Zr collisions is sensitive to the medium evolution. The charmonium production provides an independent probe to study the nucleon distribution in the isobar system.