Small carbon clusters produced by laser ablation of a carbon rod are trapped in solid parahydrogen at 4.8 K. Infrared spectra show the presence of C-3, C-5, C-9, and a few new clusters. The observed vibrational spectra with multiplet structures are tentatively associated with hindered rotation of the clusters. Temperature dependence of the IR spectra reveals the diffusion of C-3 and C-5 clusters in the crystal at around 8 K, while no diffusion of C-9 and the larger clusters is noticed. Any hydrocarbons which might be produced by reactions between the carbon clusters and the substrate hydrogen molecules are not observed both during the deposition and after the thermal annealing.