P -wave magnets exhibit odd-parity spin polarization in momentum space while retaining zero net magnetization, offering a promising route toward nonrelativistic spintronics. Previously reported p-wave magnets based on combined time-reversal and lattice-translation symmetry, Tt, have thus far exhibited ordering temperatures below the liquid-nitrogen range. Here, we demonstrate a distinct route to a pristine p-wave magnetism that does not require T t symmetry, and instead is based on incommensurate spin-spiral order. Specifically, the cycloidal magnetic structure of the multiferroic BiFeO3 (BFO) intrinsically realizes p-wave magnetism coexisting with ferroelectric polarization at room temperature. Combining symmetry analysis, density-functional-theory calculations, and circular photogalvanic-effect (CPGE) measurements, we find a large nonrelativistic spin splitting of approximately 100 meV associated with the cycloidal order. The resulting p-wave spin polarization gives rise to a characteristic CPGE response whose sign can be reversibly switched by electrically controlling the cycloid chirality. Our results establish ferroelectric BiFeO3 as a room-temperature platform for electrically switchable p-wave magnetism and provide a route toward voltage-controlled spintronic devices based on parity-breaking magnetic order.