We study non-Fermi liquid effects due to the exchange of unscreened magnetic gluons in the normal phase of high density QCD by using an effective field theory. A one-loop calculation gives the well-known result that magnetic gluons lead to a logarithmic enhancement in the fermion self-energy near the Fermi surface. The self-energy is of the form Sigma(omega)similar toomegagammalog(omega), where omega is the energy of the fermion, gamma=O(g(2)), and g is the coupling constant. Using an analysis of the Dyson-Schwinger equations we show that, in the weak coupling limit, this result is not modified by higher order corrections even in the regime where the logarithm is large, gammalog(omega)similar to1. We also show that this result is consistent with the renormalization group equation in the high density effective field theory.