The organization of actin filaments into bundles is required for cellular processes such as motility, morphogenesis, and cell division. Filament bundling is controlled by a network of actin-binding proteins. Recently, several proteins that comprise this network have been found to undergo liquid-liquid phase separation. How might liquid-like condensates contribute to filament bundling? Here, we show that the processive actin polymerase and bundling protein, VASP, forms liquid-like droplets under physiological conditions. As actin polymerizes within VASP droplets, elongating filaments partition to the edges of the droplet to minimize filament curvature, forming an actin-rich ring within the droplet. The rigidity of this ring is balanced by the droplet's surface tension, as predicted by a continuum-scale computational model. However, as actin polymerizes and the ring grows thicker, its rigidity increases and eventually overcomes the surface tension of the droplet, deforming into a linear bundle. The resulting bundles contain long, parallel actin filaments that grow from their tips. Significantly, the fluid nature of the droplets is critical for bundling, as more solid droplets resist deformation, preventing filaments from rearranging to form bundles. Once the parallel arrangement of filaments is created within a VASP droplet, it propagates through the addition of new actin monomers to achieve a length that is many times greater than the initial droplet. This droplet-based mechanism of bundling may be relevant to the assembly of cellular architectures rich in parallel actin filaments, such as filopodia, stress fibers, and focal adhesions.