The tricarbon C3 molecule has been detected in a number of translucent interstellar clouds via its $A^1\Pi_{u}-X^1\Sigma_{g}^{+}$ (000-000) electronic ‘comet’ band around 4051 Å. So far, it is the largest molecule unambiguously identified in the diffuse interstellar medium. In this work, rotationally resolved laboratory spectra are presented for the corresponding transition of the 13C3 isotopologue. The spectra are recorded in direct absorption using cavity ring-down spectroscopy in combination with a supersonic plasma jet. A rotational analysis yields accurate spectroscopic parameters. In contrast to 12C3, no significant perturbations are found for (e− or f-parity) levels up to J' = 18 in the A1Π upper electronic state.