Symmetry plays a central role in determining the polarization of spin currents induced by electric fields. It also influences how these spin currents generate spin-transfer torques in magnetic devices. Here we show that an out-of-plane damping-like torque can be generated in ruthenium dioxide (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. A maximum out-of-plane damping-like spin torque efficiency per unit electric field of 7 ± 1 × 103 Ω−1 m−1 is measured at room temperature. The observed angular dependence indicates that this is an antiferromagnetic spin Hall effect with symmetries that are distinct from other mechanisms of spin-current generation reported in antiferromagnetic and ferromagnetic materials. © 2022, The Author(s), under exclusive licence to Springer Nature Limited.