Social interaction is the new frontier in contemporary robotics: we want to build robots that blend with ease into our daily social environments, following their norms and rules. The cognitive skill that bootstraps social awareness in humans is known as "intention reading" and it allows us to interpret other agents’ actions and assign them meaning. Given its centrality for humans, it is likely that intention reading will foster the development of robotic social understanding. In this paper, we present an artificial cognitive architecture for intention reading in human-robot interaction (HRI) that makes use of social cues to disambiguate goals. This is accomplished by performing a low-level action encoding paired with a high-level probabilistic goal inference. We introduce a new clustering algorithm that has been developed to differentiate multi-sensory human social cues by performing several levels of clustering on different feature-spaces, paired with a Bayesian network that infers the underlying intention. The model has been validated through an interactive HRI experiment involving a joint manipulation game performed by a human and a robotic arm in a toy block scenario. The results show that the artificial agent was capable of reading the intention of its partner and cooperate in mutual interaction, thus validating the novel methodology and the use of social cues to disambiguate goals, other than demonstrating the advantages of intention reading in social HRI.