  We study the Sivers asymmetry in inelastic $J/\psi$ leptoproduction,
$ep^\uparrow \to e+ J/\psi+X$, within a transverse momentum dependent scheme,
the so-called generalized parton model (GPM). The effects of final-state
interactions are properly taken into account by employing the color-gauge
invariant GPM (CGI-GPM). For the $J/\psi$ formation the non-relativistic QCD
(NRQCD) framework is adopted. Predictions for unpolarized cross sections and
maximized Sivers asymmetries at EIC energies are given.
