Sivers Effect and Transverse Single Spin Asymmetry in $e+p^\uparrow \to e+J/\psi+X$

We discuss the possibility of using electroproduction of $J/\psi$ as a probe of gluon Sivers function by measuring single spin asymmetry (SSA) in experiments with transversely polarized protons and electron beams. We estimate SSA for JLab, HERMES, COMPASS and eRHIC energies using the color evaporation model of charmonium production and find asymmetry up to 25% for certain choices of model parameters which have been used earlier for estimating SSA in the SIDIS and Drell-Yan processes.