  We propose measurement of transverse single spin asymmetry (SSA) in
charmonium production as a probe of gluon Sivers function. We estimate SSA in
low virtuality electroproduction of $J/\psi $ using color evaporation model of
charmonium production and existing models of the gluon Sivers function and find
sizable asymmetry at JLab, HERMES, COMPASS and eRHIC energies.
