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.