Nowadays, the diffusion of information through social networks is a powerful phenomenon. One common way to model diffusions in social networks is the Independent Cascade (IC) model. Given a set of infected nodes according to the IC model, a natural problem is the source detection problem, in which the goal is to identify the unique node that has started the diffusion. Maximum Likelihood Estimation (MLE) is a common approach for tackling the source detection problem, but it is computationally hard. In this work, we propose an efficient method for the source detection problem under the MLE approach, which is based on computing the stationary distribution of a Markov chain. Using simulations, we demonstrate the effectiveness of our method compared to other state-of-the-art methods from the literature, both on random and real-world networks.