New coupled-state R-matrix calculations are performed at energies up to 1 eV to give rotational excitation and de-excitation cross-sections for electron collisions with CH⁺. Rotational excitations with δ j up to 7 are considered. Transitions with δ j up to 6 are found to have appreciable cross-sections, those with δ j = 2 being comparable to (indeed slightly larger than) those with δ j = 1, the only ones considered previously. Rates for electron temperatures up to 15 000 K and critical electron densities are given. A model of CH⁺ rotational populations shows them to be relatively insensitive to electron temperatures in the range 800–2000 K, but to depend strongly upon electron density. The models predict a significant population in rotational states with j > 1 even at low electron densities; at higher densities the possibility exists that electron collisions alone might explain the recently observed populations in the planetary nebula NGC 7027.