An intriguingly high abundance of both ThC13+ and UC13+ cluster cations was observed in a previous mass spectrometry experiment; however, the structural identification of these cations has not yet been completed. In this study, we determined the lowest lying structures of ThC13+ and UC13+ clusters using an unbiased structural search method. The 13-coordinate planar ring configuration was the most stable for both ThC13+ and UC13+ cluster cations. The C-An bonds in ThC13+ and UC13+ show a small degree of covalency, originating from the overlap of the s, d, and f orbitals of the An atoms with C 2p orbitals of both π and σ characteristics. The infrared and electronic absorption spectra of the most favorable planar ring configurations were theoretically simulated to facilitate the identification of the molecular structures in future experiments. This study provides an in-depth understanding of the experimental mass spectra.