We present a study of the decays B+→ρ+γ, B0→ρ0γ, and B0→ωγ. The analysis is based on data containing 347×106 BB̄ events recorded with the BABAR detector at the PEP-II asymmetric B factory. We measure the branching fractions B(B+→ρ+γ)=(1.10-0.33+0.37±0.09)×10-6 and B(B0→ρ0γ)=(0.79-0.20+0.22±0.06)×10-6, and set a 90% C.L. upper limit B(B0→ωγ)<0.78×10-6. We also measure the isospin-averaged branching fraction B(B→(ρ/ω)γ)=(1.25- 0.24+0.25±0.09)×10-6, from which we determine |Vtd/Vts|=0.200-0. 020+0.021±0.015, where the first uncertainty is experimental and the second is theoretical. © 2007 The American Physical Society.