A first search for $CP$ violation in the Cabibbo-suppressed $\Xi c+\to pK-\pi +$ decay is performed using both a binned and an unbinned model-independent technique in the Dalitz plot. The studies are based on a sample of proton-proton collision data, corresponding to an integrated luminosity of $3.0 fb-1$, and collected by the LHCb experiment at centre-of-mass energies of $7$ and $8 TeV$. The data are consistent with the hypothesis of no $CP$ violation.