The influence of the electron spin degree of freedom on nonperturbative electron-positron pair production by high-energy proton impact on an intense laser field of circular polarization is analyzed. Predictions from the Dirac and Klein-Gordon theories are compared and a spin-resolved calculation is performed. We show that the various spin configurations possess very different production probabilities and discuss the transfer of helicity in this highly nonlinear process. Our predictions could be tested by combining the few-TeV proton beam at CERN-LHC with an intense laser pulse from a table-top petawatt laser source.