In the past, it has generally been assumed that polarization observations made with ground-based telescopes are unaffected by the passage of light through the Earth's atmosphere. Here, we report observations with a new high-sensitivity astronomical polarimeter (PlanetPol) made during a Saharan dust event over the La Palma observatory in 2005 May that show excess linear polarization in the horizontal direction due to the passage of the starlight through the dust. The polarization reached a maximum value of 4.8 × 10−5 at 56° zenith distance and varied over five nights in proportion to the change in dust optical depth. Polarization of transmitted light (dichroism) does not occur for spherical or randomly oriented non-spherical particles. Thus, these results imply that some fraction of the dust grain population aligns with a preferred orientation. We use T-matrix models to demonstrate that the observed polarization direction implies a vertical orientation for the long axis of the particles. We suggest a possible mechanism for vertical orientation resulting from the electric field in the atmosphere. These results will need to be taken into account in the design and use of future instruments for high-sensitivity astronomical polarimetry. The results also indicate possible new approaches to studying aerosol particles and their effects on the Earth's atmosphere.