Integration of resistive switching and rectification functions in a single memory device is promising for high writing/readout accuracy with a simplified device architecture, but the realization remains challenging, especially with a low voltage operation. Herein, we developed self-rectifying resistive memory with a single memristive layer that can be operated at ultralow voltages with an excellent rectification ratio. The memristive layer consisted of a phase-separated lateral heterostructure of a ferroelectric polymer, poly(vinylidene fluoride-<i>co</i>-trifluoroethylene) [P(VDF-TrFE)], and a 2D halide perovskite, butylammonium lead iodide (BA₂PbI₄), which could be readily fabricated by spin-casting. Systematic characterization revealed that a lateral ferroelectric polarization from self-poled P(VDF-TrFE) could rectify the current flow into the BA₂PbI₄ channel. The resistive memory consisting of Ag/P(VDF-TrFE):BA₂PbI₄/indium tin oxide exhibited a high resistance switching ratio of >10⁶ programmable at ±0.4 V and an excellent rectification ratio of >10⁶ at ±0.1 V, along with a long data retention and stable endurance cycles.