Nonreciprocal transport, where the left-to-right-flowing current differs from the right-to-left-flowing one, is an unexpected phenomenon in bulk crystals. BiTeBr is a noncentrosymmetric material, with a giant Rashba spin-orbit coupling which presents this unusual effect when placed in an in-plane magnetic field. It has been shown that this effect depends strongly on the carrier density; however, in situ tuning has not yet been demonstrated. We developed a method where thin BiTeBr flakes are gate tuned via ionic-liquid gating through a thin protective hexagonal boron nitride layer. Tuning the carrier density allows a more than 400% variation of the nonreciprocal response in our sample. Our study demonstrates how a few-atomic-layer-thick van der Waals protection layer allows ionic gating of chemically sensitive, exotic nanocrystals.