The electronic structures of the 10 K layered yttrium carbide halide superconductor Y2C2I2 is characterized by bands of low dispersion and narrow peak-valley features in the electronic density of states at the Fermi level. In order to investigate to what extent the superconducting properties can be modified by external pressure we have studied the pressure dependence of the superconducting critical temperature and the crystal structure of Y2C2I2 to pressures of 7.4 GPa. Up to ~2.5 GPa we observe an increase of T c from 10 K to about 12 K. A structural phase transition from a 1s to a 3s stacking variant occurs at about 2.5 GPa above which T c rapidly decreases to a value of ~7.5 K at 7.5 GPa. Density functional calculations corroborate the structural phase transition to occur at a critical cell volume of ~270 Å(3) corresponding to a pressure of ~2.4 GPa, in good agreement with the experimental findings. The pressure dependence of T c and inter-atomic distances and angles are discussed with respect to the results of density functional calculations of the electronic and crystal structure.