Ambipolar diffusion (ion-neutral drift) is believed to be one of the key processes in star formation, regulating the rate of collapse of cloud cores. A by-product of the diffusion process is collisional alignment of dust grains in molecular clouds, and this can be tested observationally. We have searched for velocity differences between neutral and ionic molecular lines in three star-forming cloud cores (W3, S106 and NGC 7538), and found increases in the ion-neutral drift speed with higher degrees of submillimetre polarization (and hence grain alignment efficiency). However, the velocity differences are only ∼ 0.5 km s−1 even in the most polarized cores (p ≈ 3 per cent), a result which favours grain axial ratios a/b ∼ 0.25, while the maximum observed polarizations require larger a/b values, approximately ≥ 0.7. The number of sources observed is small, but the results suggest that ion-neutral drift does occur in magnetized star-forming cores, although grains may be aligned at surprisingly low drift speeds.