We compute the electromagnetic properties of Xi_cc baryons in 2+1 flavor Lattice QCD. By measuring the electric charge and magnetic form factors of Xi_cc baryons, we extract the magnetic moments, charge and magnetic radii as well as the Xi_cc Xi_cc rho coupling constant, which provide important information to understand the size, shape and couplings of the doubly charmed baryons. We find that the two heavy charm quarks drive the charge radii and the magnetic moment of Xi_cc to smaller values as compared to those of, e.g., the proton.