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ABSTRACT Recent (sub)millimetre polarization observations of protoplanetary discs reveal toroidally aligned, effectively prolate dust grains large enough (at least $$\sim 100$$\mu$$m) to efficiently scatter millimetre light. The alignment mechanism for these grains remains unclear. We explore the possibility that gas drag aligns grains through gas–dust relative motion when the grain’s centre of mass is offset from its geometric centre, analogous to a badminton birdie’s alignment in flight. A simple grain model of two non-identical spheres illustrates how a grain undergoes damped oscillations from flow-induced restoring torques which align its geometric centre in the flow direction relative to its centre of mass. Assuming specular reflection and subsonic flow, we derive an analytical equation of motion for spheroids where the centre of mass can be shifted away from the spheroid’s geometric centre. We show that a prolate or an oblate grain can be aligned with the long axis parallel to the gas flow when the centre of mass is shifted along that axis. Both scenarios can explain the required effectively prolate grains inferred from observations. Application to a simple disc model shows that the alignment time-scales are shorter than or comparable to the orbital time. The grain alignment direction in a disc depends on the disc (sub-)structure and grain Stokes number (St) with azimuthal alignment for large St grains in sub-Keplerian smooth gas discs and for small St grains near the gas pressure extrema, such as rings and gaps.