The polarization of Al-34 fragments, produced by single neutron pickup from a Be-9 target by a S-36 projectile at 77.5 MeV/nucleon, have been observed at GANIL via the detection of resonantly destroyed beta-asymmetry. The reaction-induced polarization is deduced using a tentative spin/parity assignment for the Al-34 ground state. A positive polarization was measured near the peak of the Al-34 yield curve. A kinematical model based on the spectator-participant model for projectile fragmentation reactions has been extended in order to take into account the features of pickup reactions, i.e., the picked-up nucleon having an average momentum equal to the Fermi momentum and aligned along the incident beam direction. The trend-line in the observed spin-orientation is very well reproduced by this model.