Molecular R‐matrix calculations are performed to give rotational excitation rates for electron collisions with linear molecular ions. Results are presented for CO+, HCO+, NO+ and H2+ up to electron temperatures of 10 000 K. De‐excitation rates and critical electron densities are also given. It is shown that the widely used Coulomb–Born approximation is valid for Δj=1 transitions when the molecular ion has a dipole greater than about 2D, but otherwise is not reliable for studying electron‐impact rotational excitation. In particular, transitions with Δj>1 are found to have appreciable rates and are found to be entirely dominated by short‐range effects.