We present the theory of site-directed dichroism and its application to the determination of rotational and orientational constraints for oriented polypeptides such as transmembrane helices. Infrared spectroscopy dichroism measurements of single amide I vibrational modes corresponding to C-13-labeled sites within the polypeptide contain information about the helix tilt and rotation angles. This information is readily extracted by analysis of the dichroism of a set of sites along the peptide sequence; Data for just two consecutive sites in the dimeric transmembrane domain of glycophorin A yield the tilt of the helix axis with respect the membrane normal and the rotation of the helix about its axis. By using dichroism data from three consecutive sites, the helix orientation parameters and the orientation of the amide I transition dipole moment, a, can be obtained; the parameters are in close agreement with the solution NMR structure of the glycophorin A peptide dimer and literature values for a. The approach provides orientational information about selectively labeled peptides even under conditions of modest fractional sample order.