In this paper, the design and robust scheduling of a nano-satellite (nanosat) swarm is presented for synthetic aperture radar (SAR) applications. Based on the power budget and bandwidth limit of nanosats, the nanosats' form factor and swarm size are chosen to ensure that requirements on ground resolution and signal-to-noise ratio are met. Next, an energy-efficient and robust scheduling considering stochastic failures is proposed using scenario optimization with convexification. The effectiveness of our proposed scheduling approach is verified with mathematical rigor as well as extensive simulation results on a realistic SAR application using strip and spot modes.