We report results from a study of the spin and parity of Ξc(2970)+ using a 980 fb-1 data sample collected by the Belle detector at the KEKB asymmetric-energy e+e- collider. The decay angle distributions in the chain Ξc(2970)+→Ξc(2645)0π+→Ξc+π-π+ are analyzed to determine the spin of this charmed-strange baryon. The angular distributions strongly favor the Ξc(2970)+ spin J=1/2 over 3/2 or 5/2, under an assumption that the lowest partial wave dominates in the decay. We also measure the ratio of Ξc(2970)+ decay branching fractions R=B[Ξc(2970)+→Ξc(2645)0π+]/B[Ξc(2970)+→Ξc′0π+]=1.67±0.29(stat)-0.09+0.15(syst)±0.25(IS), where the last uncertainty is due to possible isospin-symmetry-breaking effects. This R value favors the spin-parity JP=1/2+ with the spin of the light-quark degrees of freedom sl=0. This is the first determination of the spin and parity of a charmed-strange baryon.