Recent experiments on switching antiferromagnetic domains by electric current pulses have attracted a lot of attention to spin-orbit torques in antiferromagnets. In this work, we employ the tight-binding model solver, kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model combines spin-orbit interaction, local s-d-like exchange, and scattering of conduction electrons on on-site disorder potential to provide a microscopic mechanism for angular-momentum relaxation. We consider two versions of the model: One with preserved and one with broken sublattice symmetry. A nonequilibrium staggered polarization that is responsible for the so-called Neél spin-orbit torque is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, antidamping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, antidamping torques also reveal a sizable dependence on impurity concentration. Our numerical analysis also confirms symmetry classification of spin-orbit torques and strong torque anisotropy due to in-plane confinement of electron momenta.