We present an algorithm to compute molecular graph descriptors considering the stereochemistry of the molecular structure based on our previously introduced signature molecular descriptor. The algorithm can generate two types of descriptors, one which is compliant with the Cahn-Ingold-Prelog priority rules, including complex stereochemistry structures such as fullerenes, and a computationally efficient one based on our previous definition of a directed acyclic graph that is augmented to a chiral molecular graph. The performance of the algorithm in terms of speed as a canonicalizer as well as in modeling and predicting bioactivity is evaluated, showing an overall better performance than other molecular descriptors, which is particularly relevant in modeling stereoselective biochemical reactions. The complete source code of the stereo signature molecular descriptor is available for download under an open-source license at http://molsig.sourceforge.net.