The orientation of molecular chains in polymers cannot be easily extracted from ATR spectra measurements. One can infer the orientation parameters by using plausible models that describe the type of the statistical distribution of the molecular chains in the sample. in this work, we are interested in the case of weakly aligned polymers. Therefore, we first adjusted the partial axial orientation model usually applied for strongly oriented polymers to the samples under our investigations and second, related the parameters describing the orientation configuration to the dichroic ratios in four particular molecular chain distributions : randomly, totally, partially, and elliptically oriented. A new method that leads to the determination of these dichroic ratios from ATR spectra is presented. This method is based only on the use of three distinct polarizations of the beam. Thus, all the practical difficulties usually encountered in the other methods are eliminated.