Using techniques of delayed pulsed-field ionization zero-kinetic-energy (ZEKE) photoelectron spectroscopy, we have resolved spin-orbit structure in the rotational profile of the origin band in the non-resonant two-photon threshold photoionization of propyne. Both the rotational and spin-orbit characteristics of this band are well-simulated by a simple model that assumes the spin-orbit splitting of acetylene cation in combination with the rotational constants of the neutral propyne ground state. This result, combined with very little evidence for photoionizing transitions terminating on vibronically excited states, suggests that the structure of the propyne cation structure is very close to that of the neutral ground state and very little altered by Jahn-Teller distortion.