We investigate J/ψ photoproduction asymmetries in the framework of the
NRQCD factorization approach. It is shown that the color octet contribution
leads to large uncertainties in the predicted asymmetries which rules out the
possibility to precisely measure the gluon polarization in the nucleon through
this final state. For small values of the color octet parameters being
compatible with J/ψ photoproduction data it appears possible that a
measurement of J/ψ asymmetries could provide a new test for the NRQCD
factorization approach, on one hand, or a measurement of the polarized gluon
distribution from low inelasticity events (z<0.7), on the otherComment: 12 pages, LaTeX, with 6 figs. Final version published in Phys.Rev.