We present a calculation of inelastic J/psi production in polarized photon-
hadron collisions. We consider the photoproduction of J/psi in the energy r
ange relevant to the DESY HERA collider. The Weizsacker-Williams approximat
ion is adapted in the evaluation of the cross sections for ep collisions. W
e find that this process can give another independent test for the color-oc
tet mechanism, and the different features for the two color-octet processes
may provide further information on the mechanism for inelastic J/psi photo
production. The discrepancy in the production asymmetry A between various s
ets of polarized gluon distribution functions is also found to be distincti
ve.