Antiferromagnetic materials have unique properties due to their alternating spin arrangements. Their compensated magnetic order, robust against external magnetic fields, prevents long-distance crosstalk from stray fields. Furthermore, antiferromagnets with combined parity and time-reversal symmetry enable electrical control and detection of ultrafast exchange-field enhanced spin manipulation up to THz frequencies. Here we report the experimental realization of a nonvolatile antiferromagnetic memory mimicking an artificial synapse, in which the reconfigurable synaptic weight is encoded in the ratio between reversed antiferromagnetic domains. The non-volatile memory is “written” by spin-orbit torque-driven antiferromagnetic domain wall motion and “read” by nonlinear magnetotransport. We show that the absence of long-range interacting stray magnetic fields leads to very reproducible electrical pulse-driven variations of the synaptic weights.