Large-scale four-component relativistic calculations have been carried out for excited states of the tris-(allyl)-iridium complex, Ir(C3H5)3, using the relativistic polarization propagator method. The main focus was on providing insight into the lowest excited states of the three different structural forms of the complex, C3, C3h, and C1, including prediction of the excitation spectra and elucidation of spin-orbit coupling (SOC) effects for these forms. To unravel SOC effects, results of spin-orbit (SO) calculations were contrasted to results of spin-free (SF) calculations. Both the SO and SF calculations predict the lowest excited states of all three forms are of Rydberg type. We identified several Rydberg series, characterized by different hole configurations, that constitute the low-energy parts of the SO and SF excitation spectra. The SO spectra, however, differ notably from the corresponding SF spectra, pointing out to the influence of SOC. The most pronounced differences are observed for the SO and SF spectra of the C3h form. Our analysis indicates that SOC in this form causes strong alterations of the frontier occupied orbitals, participating in the excitations. As a result, excited states belonging to the first two Rydberg series are characterized by different electronic structure (hole configurations) in the SO and SF cases. Besides the orbital alteration effect, two other SOC effects, zero-field splitting and singlet-triplet mixing were identified in the SO spectra of all three forms. These effects result in new lines in the SO spectra and notable redistribution of the spectral intensity.