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The interplay between electronic transport and antiferromagnetic order has attracted a surge of interest as recent studies show that a moderate change in the spin orientation of a collinear antiferromagnet may have a significant effect on the electronic band structure. Among numerous electrical probes to read out such a magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit-coupled systems. However, UMR has never been observed in antiferromagnets before, given the absence of intrinsic spin-dependent scattering. Here, we report a UMR in the antiferromagnetic phase of a FeRh/Pt bilayer, which undergoes a sign change and then increases strongly with an increasing external magnetic field, in contrast to UMRs in ferromagnetic and nonmagnetic systems. We show that Rashba spin-orbit coupling alone cannot explain the sizable UMR in the antiferromagnetic bilayer and that field-induced spin canting distorts the Fermi contours to greatly enhance the UMR by 2 orders of magnitude. Our results can motivate the growing field of antiferromagnetic spintronics and suggest a route to the development of tunable antiferromagnet-based spintronics devices.