Vibrational spectroscopy using polarized incident radiation can be used to determine the orientation of X-H bonds with respect to coordinates such as crystallographic axes. The adaptation of this approach to polymer fibers is described here. It requires spectral intensity to be quantified around a 180 degrees range of polarization angles and not just recorded transversely and longitudinally as is normal in fiber spectroscopy. Mercerized cellulose II is used as an example. The unit cell of the cellulose II lattice contains six distinct hydroxyl groups engaged in a complex network of hydrogen bonds that hold the cellulose chains laterally together. A formalism is described to relate the variation in intensity of each O-H stretching mode to the angle between its transition moment and the chain axis as the polarization axis is rotated with respect to the fiber axis. It was necessary to include the effect of dispersion in chain orientation around the mean and the averaging of all rotational positions of the chains round their axis. The two crystallographically distinct O(2)-H groups, which are each hydrogen-bonded to only one acceptor oxygen, show a close match in orientation between the transition moments of their stretching bands and the O-H bond axis. The two O(3)-H groups each have a three-centered hydrogen bond to O-5 and O-6 of the next residue in the same chain. The transition moments of their stretching modes lay between the acceptor oxygens. Hydrogen bonding from the O(6)-H groups is still more complex but again the transition moment of each O-H bond lay within the cone of orientations described by the acceptor oxygens, provided that one additional acceptor oxygen excluded from the published crystal structure was considered. The transition moments for the O-H stretching modes were approximately aligned with the O-H bond axes, but the alignment was not necessarily exact. This approach is not restricted to hydroxyl groups, but it is particularly useful for the elucidation of hydrogen bonding in fibrous polymers for which crystallographic data on proton positions are not available.