In this work, we use the framework of effective field theory to couple Einsteins Gravity to Quantum Electrodynamics (QED) and determine the gravitational corrections to the two-loop beta function of the electric charge. Our results indicate that gravitational corrections do not alter the running behavior of the electric charge; on the contrary, we observe that it gives a positive contribution to the beta function, making the electric charge grow faster. The opposite occurs to the $lambda$ beta function in the Einstein-Scalar-QED system, where at one-loop order we observe that gravity gives a negative contribution to the $lambda$ beta function, indicating that, if the scalar particle has a mass a few orders below Planck scale, $lambda$ can be asymptotically free.
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