We present estimates of Single Spin Asymmetry (SSA) in the electroproduction of J/ψ taking into account the transverse momentum dependent (TMD) evolution of the gluon Sivers function. We estimate SSA for JLab, HERMES, COMPASS and eRHIC energies using color evaporation model of J/ψ. We have calculated the asymmetry using recent parameters extracted by Echevarria et al. using the CSS approach to TMD evolution. These recent TMD evolution fits are based on the evolution kernel in which the perturbative part is resummed up to next-to-leading logarithms (NLL) accuracy. We have also estimated the asymmetry by using parameters which had been obtained by a fit by Anselmino et al., using both an exact numerical and an approximate analytical solution of the TMD evolution equations. We find that the variation among the different estimates obtained using TMD evolution is much smaller than between these on one hand and the estimates obtained using DGLAP evolution on the other. Even though the use of TMD evolution causes an overall reduction in asymmetries compared to the ones obtained without it, they remain sizable. Overall, upon use of TMD evolution, predictions for asymmetries stabilize.