We propose to use logarithmic spiral resonators for efficient absorption of microwaves. By combining their scale invariant geometries and Fabry-Perot-type resonances stemming from the fundamental TM mode, we realize a microwave metasurface with broadband absorption performance. The metasurface comprises logarithmic spiral resonators backed with a metallic surface and it can absorb >95% of incident microwave energy within the frequency range of 6 GHz - 37 GHz. We discuss the physics underlying the broadband absorption and the crucial role of vortex energy flow. The study opens a new direction of electromagnetic wave absorption by employing the scale invariance of Maxwell equations.