We propose a test based on direct detection data that allows us to determine if the dark matter particle is different from its antiparticle. The test requires the precise measurement of the dark matter spin-independent direct detection cross sections off three different nuclei and consists of interpreting such signals in terms of self-conjugate ($\text{particle}=\text{antiparticle}$) dark matter to see if such interpretation is consistent. If it is not, the dark matter must be different from its antiparticle. We illustrate this procedure for two sets of target nuclei, ${\mathrm{Xe},\mathrm{Ar},\mathrm{Si}}$ and ${\mathrm{Xe},\mathrm{Ar},\mathrm{Ge}}$, identifying the regions of the parameter space where it is particularly feasible. Our results indicate that future signals in direct detection experiments, if sufficiently accurate, might be used to establish that the dark matter particle is not its own antiparticle---a major step towards the determination of the fundamental nature of the dark matter.