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We present measurements of the differential cross section d I / d p T gamma for the associated production of a c-quark jet and an isolated photon with rapidity | y gamma | 15 GeV . The ratio of differential cross sections for gamma + c to gamma + b production as a function of p T gamma is also presented. The results are based on data corresponding to an integrated luminosity of 8.7 fb - 1 recorded with the D0 detector at the Fermilab Tevatron p p A= Collider at s = 1.96 TeV . The obtained results are compared to next-to-leading order perturbative QCD calculations using various parton distribution functions, to predictions based on the k T -factorization approach, and to predictions from the sherpa and pythia Monte Carlo event generators.