The prediction of single-spin asymmetry in inelastic photoproduction of J/psi in ep(up arrow) collision is presented. At next-to-leading order, the dominating process is photon-gluon fusion, gamma + g -> J/psi + g for the production of J/psi in e + p(up arrow) -> J/psi + X, which directly probes the gluon Sivers function. Using the nonrelativistic QCD based color octet model, the color octet states S-3(1)(8), S-1(0)(8) and P-3(J(0,1,2))(8) contribution to J/psi production is calculated. Sizable asymmetry is estimated as a function of transverse momentum P-T and energy fraction z of J/psi in the range 0 < P-T <= 1 GeV and 0.3 < z <= 0.9. The unpolarized differential cross section of inelastic J/psi photoproduction is found to be in good agreement with H1 and ZEUS data.
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