Reaction rate constants and cross sections are computed for the radiative association of carbon cations (C+) and fluorine atoms (F) in their ground states. We consider reactions through the electronic transition 11Π → X1Σ+ and rovibrational transitions on the X1Σ+ and a3Π potentials. Semiclassical and classical methods are used for the direct contribution and Breit-Wigner theory for the resonance contribution. Quantum mechanical perturbation theory is used for comparison. A modified formulation of the classical method applicable to permanent dipoles of unequally charged reactants is implemented. The total rate constant is fitted to the Arrhenius-Kooij formula in five temperature intervals with a relative difference of <3%. The fit parameters will be added to the online database KIDA. For a temperature of 10-250 K, the rate constant is about 10-21 cm3 s-1, rising toward 10-16 cm3 s-1 for a temperature of 30 000 K.