  Recent (sub)millimeter polarization observations of protoplanetary disks
reveal toroidally aligned, effectively prolate dust grains large enough (at
least ~100 $\mu$m) to efficiently scatter millimeter 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 center of
mass is offset from its geometric center, 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 center in the flow direction
relative to its center of mass. Assuming specular reflection and subsonic flow,
we derive an analytical equation of motion for spheroids where the center of
mass can be shifted away from the spheroid's geometric center. We show that a
prolate or an oblate grain can be aligned with the long axis parallel to the
gas flow when the center of mass is shifted along that axis. Both scenarios can
explain the required effectively prolate grains inferred from observations.
Application to a simple disk model shows that the alignment timescales are
shorter than or comparable to the orbital time. The grain alignment direction
in a disk depends on the disk (sub-)structure and grain Stokes number (St) with
azimuthal alignment for large St grains in sub-Keplerian smooth gas disks and
for small St grains near the gas pressure extrema, such as rings and gaps.
