Single-walled carbon nanotubes (SWCNTs) are reported to spontaneously align in a rotational pattern by drying a liquid droplet of toluene containing polyfluorene as a dispersant. By situating a droplet of an SWCNT solution around a glass bead, spiral patterns are generated. The parallel alignment of SWCNTs along one stripe of such a pattern is confirmed using scanning electron microscopy and polarized optical microscopy. The orientation order increases toward the outer edge of a stripe. The stripe width in the pattern is proportional to the solute concentration, and the width and position of the stripes follow geometric sequences. The growth of the rotational pattern is also observed in real time. The process of spiral pattern formation is visualized, indicating the role of the annihilation of counter-traveling accompanied by continuous depinning. The geometric sequences for the stripe width and position are explained by the near-constant traveling speed and solute enrichment at the droplet periphery.