The ratio of the proton's electric to magnetic form factor, G_E/G_M, can be extracted in elastic electron-proton scattering by measuring either cross sections, beam-target asymmetry or recoil polarization. Separate determinations of G_E/G_M by cross sections and recoil polarization observables disagree for Q^2 > 1 (GeV/c)^2. Measurement by a third technique might uncover an unknown systematic error in either of the previous measurements. The beam-target asymmetry has been measured for elastic electron-proton scattering at Q^2 = 1.51 (GeV/c)^2 for target spin orientation aligned perpendicular to the beam momentum direction. This is the largest Q^2 at which G_E/G_M has been determined by a beam-target asymmetry experiment. The result, \muG_E/G_M = 0.884 +/- 0.027 +/- 0.029, is compared to previous world data.