The syntheses of interstellar c-C3H2, H2CCC, c-C3H, and HCCC, where "c" stands for the cyclic isomer, are thought to proceed via dissociative recombination of the precursor ions c-C3H+3 and H2CCCH+, which are themselves produced mainly via the radiative association reaction between C3H+ and H2. We have utilized ab initio methods to study the potential energy surface (PES) for the association of the linear ion C3H+ and H2 to form the isomers c-C3H+3 and H2CCCH+. The overall rate coefficient for radiative association has been calculated as a function of temperature via the phase space method. Our ab initio calculations show that the H2CCCH+ isomer is formed directly without an activation barrier from reactants, and that isomerization between the two isomers can occur readily via a low-energy pathway consisting of two transition states (saddle points on the PES) and one intermediate (local minimum on the PES). Calculation of the equilibrium coefficient for the isomerization H2CCCH+ ⇔ c-C3H3+ as a function of energy shows that equal abundances of these two ions should be produced as relaxation proceeds, in agreement with experimental measurements at high pressure. Our results confirm the important point that a simple ion-molecule association reaction can produce a cyclic hydrocarbon. If dissociative recombination reactions involving c-C3H+3 and H2CCCH+ maintain the carbon skeletal structure of the ions and produce roughly similar C3H/C3>H2 branching ratios, then abundance ratios of unity are produced between the cyclic and noncyclic isomers of C3H and C3H2 via this mechanism. The large abundance ratio of c-C3H2 to H2CCC observed in TMC-1 can then be explained by differential destruction rates.