We utilize a high-mobility double-gated graphene field-effect transistor to measure the accumulated charge created by positron annihilation in its back-gate. The device consists of an exfoliated graphene flake stacked between two hexagonal boron nitride flakes placed on a 1 cm2 substrate of 500 μm thick conducting p-doped Si capped by 285 nm-thick SiO2. The device is placed in close proximity to a 780 kBq 22Na positron source emitting a constant flux of positrons. During the measurement, positrons annihilate within the back-gate, kept floating using a low-capacitance relay. The accumulated positive charge capacitively couples to the graphene device and builds a positive voltage, detectable through a shift in the top-gate dependent graphene resistance characteristic. The shift in the position of the top-gate Dirac peak is then used for extracting the exact voltage buildup and quantitative evaluation of the accumulated charge. Reaching a positron current sensitivity of ∼1.2 fA/Hz, detected over 20 min, our results demonstrate the utility of two-dimensional layered materials as probes for charging dynamics of positrons in solids.