Achieving atmospheric flight on Mars is challenging due to the low density of the Martian atmosphere. Aerodynamic forces are proportional to the atmospheric density, which limits the use of conventional aircraft designs on Mars. Here, we show using numerical simulations that a flapping wing robot can fly on Mars via bioinspired dynamic scaling. Trimmed, hovering flight is possible in a simulated Martian environment when dynamic similarity with insects on earth is achieved by preserving the relevant dimensionless parameters while scaling up the wings three to four times its normal size. The analysis is performed using a well-validated 2D Navier-Stokes equation solver, coupled to a 3D flight dynamics model to simulate free flight. The majority of power required is due to the inertia of the wing because of the ultra-low density. The inertial flap power can be substantially reduced through the use of a torsional spring. The minimum total power consumption is 188 W kg-1 when the torsional spring is driven at its natural frequency.