We present the first measurement of associated direct photon+muon production in hadronic collisions, from a sample of 1.8 TeV 𝑝⁢¯𝑝 collisions recorded with the Collider Detector at Fermilab. Quantum chromodynamics (QCD) predicts that these events are primarily from the Compton scattering process 𝑐⁢→𝑔⁡𝑐⁢𝛾, with the final state charm quark producing a muon. Hence this measurement is sensitive to the charm quark content of the proton. The measured cross section of 29 ±9 pb is compared to a leading-order QCD parton shower model as well as a next-to-leading-order QCD calculation.