Spin polarization of 37K nuclei produced via single proton pickup from a 9Be target by a beam of 150 MeV/nucleon 36Ar has been observed. Positive spin polarization with magnitude (8.5+/-0.6)% was deduced near the peak of the 37K momentum distribution. The variation of the spin polarization as a function of outgoing 37K momentum is explained by a classical conservation model, as previously applied to describe the induced spin polarization observed for fragments produced in intermediate-energy heavy-ion reactions, with the condition that the picked-up proton has an average momentum equal to the Fermi momentum and is aligned along the incident beam direction.