We have measured the cross section of γ+D*± production in p¯p collisions at s=1.8TeV using the Collider Detector at Fermilab. In this kinematic region, the Compton scattering process (gc→γc) is expected to dominate and thus provide a direct link to the charm quark density in the proton. From the 45±18 γ+D*± candidates in a 16.4pb−1 data sample, we have determined the production cross section to be 0.38±0.15(stat)±0.11(syst) nb for the rapidity range |y(D*±)|<1.2 and |y(γ)|<0.9, and for the transverse momentum range pT(D*±)>6GeV/c and 16<pT(γ)<40GeV/c. The measured cross section is compared to a theoretical prediction.