  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.
