During cytokinesis, animal cells rapidly remodel the equatorial cortex to build an aligned array of actin filaments called the contractile ring. Local reorientation of filaments by active equatorial compression is thought to underlie the emergence of filament alignment during ring assembly. Here, combining single molecule analysis and modeling in one-cell C. elegans embryos, we show that filaments turnover is far too fast for reorientation of individual filaments by equatorial compression to explain the observed alignment, even if favorably oriented filaments are selectively stabilized. By tracking single formin/CYK-1::GFP particles to monitor local filament assembly, we identify a mechanism that we call filament-guided filament assembly (FGFA), in which existing filaments serve as templates to orient the growth of new filaments. FGFA sharply increases the effective lifetime of filament orientation, providing structural memory that allows cells to build highly aligned filament arrays in response to equatorial compression, despite rapid turnover of individual filaments.