Intracellular structures and organelles such as the nucleus, the centrosome, or the mitotic spindle typically scale their size to cell size [1]. Similarly, cortical polarity domains built around the active form of conserved Rho-GTPases, such as Cdc42p, exhibit widths that may range over two orders of magnitudes in cells with different sizes and shapes [2-6]. The establishment of such domains typically involves positive feedback loops based on reaction-diffusion and/or actin-mediated vesicle transport [3, 7, 8]. How these elements may adapt polarity domain size to cellular geometry is not known. Here, by tracking the width of successive oscillating Cdc42-GTP domains in fission yeast spores [9], we find that domain width scales with local cell-surface radii of curvature over an 8-fold range, independently of absolute cell volume, surface, or Cdc42-GTP concentration. This local scaling requires formin-nucleated cortical actin cables and the fusion of secretory vesicles transported along these cables with the membrane. These data suggest that reaction-diffusion may set a minimal domain size and that secretory vesicle transport along actin cables may dilute and extend polarity domains to adapt their size to local cell-surface curvature. This work reveals that actin networks may act as micrometric curvature sensors and uncovers a generic morphogenetic principle for how polarity domains define their size according to cell morphologies. 