The trans-azobenzene molecule is thought to prefer a planar C2h geometry, in gas phase as well as in solution, according to the most recent computational studies. As a consequence, the weak n-->pi* absorption band is forbidden by symmetry at the equilibrium geometry, and its intensity depends on the effect of the vibrational motions on the electronic structure. In this computational study, we determine the contribution of the vibrational modes to the oscillator strength, taking into account the anharmonicity, the thermal distributions, and the solvent effects. The good agreement of our results with the measured absorption spectrum confirms the C2h equilibrium structure of trans-azobenzene, with a relatively easy torsion of the phenyl groups around the N--C bonds. We also address the question of the polarization of this transition, which is a preliminary step to interpret the time-resolved fluorescence anisotropy measurements [C.-W. Chang et al., J. Am. Chem. Soc., 126, 10109 (2004)], a very sensitive probe of solvent effects on the excited state dynamics.