  We calculate the lowest order quantum gravity contributions to QED beta
function in an effective field theory picture with a momentum cutoff. We use a
recently proposed 4 dimensional improved momentum cutoff that preserves gauge
and Lorentz symmetries. We find that there is non-vanishing quadratic
contribution to the photon 2-point function but that does not lead to the
running of the original coupling after renormalization. We argue that gravity
cannot turn gauge theories asymptotically free.
