Symmetry plays a central role in determining the form of electrically-generated spin torques in magnetic devices. Here, we show that an unconventional out-of-plane damping-like torque can be generated in ruthenium oxide (RuO2)/permalloy devices when the Néel vector of the collinear antiferromagnet RuO2 is canted relative to the sample plane . By measuring characteristic changes in all three components of the electric-field-induced torque vector as a function of the angle of the electric field relative to the crystal axes, we find that the RuO2 generates a spin current with a well-defined tilted spin orientation that is approximately parallel to the Néel vector. This dependence is the signature of an antiferromagnetic spin-Hall effect predicted to arise from momentum-dependent spin splitting within the bandstructure of RuO2, rather than from spin-orbit coupling . The unconventional components are absent in the isostructural but non-magnetic rutile oxide IrO2. The out-of-plane antidamping component of the spin torque from RuO2 is among the strongest measured in any material even with the antiferromagnetic domain structure uncontrolled, suggesting that high efficiencies useful for switching magnetic devices with perpendicular magnetic anisotropy might be achieved by controlling the domain structure.