We analyze the real-photon asymmetry Aγ± for the parity-violating (PV) π± production on the Δ resonance via the reactions γ⃗+p→Δ+→π++n and γ⃗+d→Δ0+p→π-+p+p. This asymmetry is nonvanishing due to a PV γNΔ coupling constant, dΔ±. We argue that an experimental determination of this coupling would be of interest for hadron dynamics, possibly shedding light on the S-wave/ P-wave puzzle in the hyperon nonleptonic decays and the violation of Hara’s theorem in weak radiative hyperon decays.