We have performed a dynamical study of the endothermic and barrierless C⁺ + H₂(¹Σ_g⁺) → CH⁺(¹Σ_g⁺) + H reaction for different initial rotational states of the H₂(v = 0) and H₂(v = 1) manifolds. The calculations have been carried out using quasiclassical trajectories and the Gaussian binning methodology on a recent potential energy surface [R. Warmbier and R. Schneider, Phys. Chem. Chem. Phys., 2011, 13, 10285]. Both state-selected integral cross sections as a function of the collision energy and rate coefficients, k_v,j(T), have been determined. We show that rotational excitation of the reactants is as effective as vibrational excitation when it comes to increasing the reactivity, and that both types of excitation could contribute to explain the unexpectedly high abundance of CH⁺ in the interstellar media. Such an increase in reactivity takes place by suppressing the reaction threshold when the internal energy is sufficient to overcome the endothermicity. Whenever this is the case, the excitation functions at collision energies E_coll ≤ 0.1 eV display a ∝E^−1/2_coll dependence. However, the absolute values of the state selected k_v=1(T) are one order of magnitude below the Langevin model predictions. The disagreement between the approximately derived experimental rate coefficients for v = 1 and those calculated by this and previous theoretical treatments is due to the neglect of the effect of the rotational excitation in the derivation of the former. In spite of the deep well present in the potential energy surface, the reaction does not show a statistical behaviour.