Accurate modeling of anionic abundances in the interstellar and circumstellar media requires calculations of collisional data with the most abundant species that are usually He atoms and H2 molecules. In this paper, we focus on smaller cyclic molecular anion, c-C3H-, an astrophysical candidate, following the detection of larger CnH- carbon chains. From a new three-dimensional potential energy surface, the rotational (de-)excitation of the c-C3H-(X1A1) anion by collision with He is investigated. The surface is obtained in the supermolecular approach at the CCSD(T)-F12/aug-cc-pVTZ level of theory. Fully quantum close-coupling calculations of inelastic integral cross sections are performed on a grid of collisional energies large enough to ensure the convergence of the state-to-state rate coefficients for the 34 first rotational levels up to jKa,Kc = 77,0 of c-C3H- and temperatures ranging from 5 to 100 K. For this collisional system, rate coefficients exhibit a strong dominance in favor of 21,2 → l1,1 downward transition. This transition was previously used for the detection of the cyclic parent c-C3H. The c-C3H--He rate coefficients (∼10-11 cm3 s-1) are of the same order of magnitude as those of the detected anions CnH- (as C2H-, C4H-, and C6H-) in collision with He and one order of magnitude smaller than those with H2. The critical densities of H2 were also estimated, and a discussion on the validity of the local thermodynamic equilibrium conditions is carried out. This work represents the contribution to understanding and modeling abundances and chemistry of hydrocarbon radicals, CnH, in astrophysical media.