Cell and tissue morphogenesis depend on the production and spatial organization of tensional forces in the actin cytoskeleton. Actin network architecture is complex because it is made of distinct modules in which filaments adopt a variety of organizations. The assembly and dynamics of these modules is well described but the self-organisation rules directing the global network architecture are much less understood. Here we investigated the mechanism regulating the interplay between network architecture and the geometry of cell’s extracellular environment. We found that α-actinin, a filament crosslinker, is essential for network symmetry to be consistent with extracellular microenvironment symmetry. It appeared to be required for the interconnection of transverse arcs with radial fibres to ensure an appropriate balance between forces at cell adhesions and across the entire actin network. Furthermore, the connectivity of the actin network appeared necessary for the cell ability to integrate and adapt to complex patterns of extracellular cues as they migrate. Altogether, our study has unveiled a role of actin-filament crosslinking in the physical integration of mechanical forces throughout the entire cell, and the role of this integration in the establishment and adaptation of intracellular symmetry axes in accordance with the geometry of extracellular cues.