The variation with microwave frequency and temperature of previously reported anomalous peaks in the EPR spectra of Mn 12 -acetate, under large transverse fields, reveals that the molecular easy magnetization axes are tilted with respect to the global symmetry direction. More importantly, on the basis of the angle dependence of fine structures observed in the EPR spectra we infer that the tilt distribution must be discrete, as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [S. Hill et al., Phys. Rev. Lett. 90, 217204 (2003)]. The tilts are confined to two orthogonal planes, and the distribution extends up to ϳ1.7°degrees away from the global easy ͑z͒ axis. We ascribe the tilting to the hydrogen-bonding effect associated with the disordered acetic acid solvent molecules. The effect is considerably larger than deduced from x-ray diffraction analyses. These data constitute the sought-after evidence for the presence of transverse fields in Mn 12 -acetate, and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low-temperature hysteresis experiments for this S =10 system.