Swarms of soft microrobots controlled by minimally invasive magnetic fields show promise as biomedical agents. The collective behavior of such swarms, governed by magnetic and hydrodynamic interactions, emerges from the properties of their individual constituents. The introduction of both magnetic and structural anisotropy into microrobots expands the possibilities for tailoring and predetermining interactions and collective behaviors that result. Unfortunately, current methods for large-scale production of soft microrobots, typically result in isotropic properties. Herein, by combining simulation-guided design and droplet-based microfluidics, we present a versatile, high-throughput technique for fabricating soft microrobots with programmable structural and magnetic anisotropy. Such microrobots consist of iron oxide nanoparticles organized into supra-domain structures and entrapped in a hydrogel matrix that can be elongated independently of its magnetic properties. By applying rotating magnetic fields to resulting swarms, distinct collective behaviors are produced, including gas-like formations, variable crystals, and heterogeneous motions.