We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov kernel; and two nodes are connected with a probability depending on a unknown function of their latent geodesic distance. We provide theoretical guarantees for the non-parametric estimation of the Markov kernel and the connection function. Proofs encompass concentration inequalities for random matrices and a recent concentration inequality for U-statistics of order 2 in a dependent framework. As a by product, we propose heuristics to solve link prediction tasks.