We present electron-impact rotational excitation calculations for polyatomic molecular ions. The theory developed in this paper is an extension of the work of Rabadán et al (Rabadán I, Sarpal B K and Tennyson J 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2077) on linear molecular ions to the case of symmetric-top species. The H3+ and H3O+ ions, as well as their deuterated forms D3+ and D3O+, are used as test cases and cross sections are obtained at various levels of approximation for impact energies up to 5 eV. As in the linear case, the widely used Coulomb–Born (CB) approximation is found to be unreliable in two major aspects: transitions with ΔJ > 1 are entirely dominated by short-range interactions and threshold effects are important at very low energies. Electron collisional selection rules are found to be consistent with the CB theory. In particular, dominant transitions are those for which ΔJ ≤ 2 and ΔK = 0
