Orientational defects are molecular-scale point defects consisting of misaligned sterically trapped molecules. Such defects have been predicted in alpha-RDX using empirical force fields. These calculations indicate that their concentration should be higher than that of vacancies. In this study we confirm the stability of a family of four orientational defects in alpha-RDX using first-principles calculations and evaluate their formation energies and annealing barrier heights. The charge density distribution in the defective molecules is evaluated and it is shown that all four orientational defects exhibit some level of charge reduction at the midpoint of the N-N bond, which has been previously related to the sensitivity to initiation of the material. We also evaluate the vibrational spectrum of the crystal containing orientational defects and observe band splitting relative to the perfect crystal case. This may assist the experimental identification of such defects by Raman spectroscopy.