The actomyosin cytoskeleton generates mechanical forces that power important cellular processes, such as cell migration, cell division, and mechanosensing. Actomyosin self-assembles into contractile networks and bundles that underlie force generation and transmission in cells. A central step is the assembly of the myosin II filament from myosin monomers, regulation of which has been extensively studied. However, myosin filaments are almost always found as clusters within the cell cortex. While recent studies characterized cluster nucleation dynamics at the cell periphery, how myosin clusters grow on stress fibers remains poorly characterized. Here, we utilize a U2OS osteosarcoma cell line with endogenously tagged myosin II to measure the myosin cluster size distribution in the lamella of adherent cells. We find that myosin clusters can grow with Rho-kinase (ROCK) activity alone in the absence of myosin motor activity. Time-lapse imaging reveals that myosin clusters grow via increased myosin association to existing clusters, which is potentiated by ROCK-dependent myosin filament assembly. Enabling myosin motor activity allows further myosin cluster growth through myosin association that is dependent on F-actin architecture. Using a toy model, we show that myosin self-affinity is sufficient to recapitulate the experimentally observed myosin cluster size distribution, and that myosin cluster sizes are determined by the pool of myosin available for cluster growth. Together, our findings provide new insights into the regulation of myosin cluster sizes within the lamellar actomyosin cytoskeleton.