  Electrical spin-current generation is among the core phenomena driving the
field of spintronics. Using {\em ab initio} calculations we show that a
room-temperature metallic collinear antiferromagnet RuO$_2$ allows for highly
efficient spin-current generation, arising from anisotropically-split bands
with conserved up and down spins along the N\'eel vector axis. The zero net
moment antiferromagnet acts as an electrical spin-splitter with a 34$^\circ$
propagation angle between spin-up and spin-down currents. Correspondingly, the
spin-conductivity is a factor of three larger than the record value from a
survey of 20,000 non-magnetic spin-Hall materials. We propose a versatile
spin-splitter-torque concept utilizing antiferromagnetic RuO$_2$ films
interfaced with a ferromagnet.
