Breast parenchymal density is considered a strong indicator of cancer risk. However, measures of breast density are often qualitative and require the subjective judgment of radiologists. This work proposes a supervised algorithm to automatically assign a BI-RADS breast density score to a digital mammogram. The algorithm applies principal component analysis to the histograms of a training dataset of digital mammograms to create four different spaces, one for each BI-RADS category. Scoring is achieved by projecting the histogram of the image to be classified onto the four spaces and assigning it to the closest class. In order to validate the algorithm, a training set of 86 images and a separate testing database of 964 images were built. All mammograms were acquired in the craniocaudal view from female patients without any visible pathology. Eight experienced radiologists categorized the mammograms according to a BIRADS score and the mode of their evaluations was considered as ground truth. Results show better agreement between the algorithm and ground truth for the training set (kappa=0.74) than for the test set (kappa=0.44) which suggests the method may be used for BI-RADS classification but a better training is required.