Social learning strategies implement a distributed decision-making process where several agents, connected over a graph, exchange their beliefs about some hypotheses of interest. Each agent uses some local model that describes the marginal distribution of its own data. Traditional strategies do not exploit any joint model across the agents, because it is usually unknown and difficult to learn in a distributed manner. We propose a novel strategy to account for the statistical dependence across the agents. Based on the theory of statistical copulas, we find a mathematical representation for the joint likelihood that is amenable to distributed implementations. Then, we exploit the exact consensus framework to develop two distributed algorithms: i) a decentralized stochastic gradient ascent algorithm to learn, during a training stage, the parameters of the statistical copula that describes the joint likelihood; and ii) a social learning algorithm to compute the likelihood needed to perform online decision-making. We show that the proposed strategy outperforms the existing strategies.