The synthesis of topological insulators (TIs) of good crystalline quality provides an attractive material platform for low power-consumption spintronic devices of relevance for non-volatile memory applications. While experimental measurements of strong spin-orbit torque (SOT) have been reported in Bi_1-xSb_x alloys, one of the earliest discovered TIs, key questions remain about the nature of SOT in this material system. We describe the synthesis of Bi_1-xSb_x thin films of good crystalline quality by molecular beam epitaxy (MBE) and the characterization of these films using in vacuo angle-resolved photoemission spectroscopy (ARPES) as well as ex situ transmission electron microscopy, x-ray diffraction, and Raman spectroscopy. ARPES measurements of samples with varying compositions allow us to track the band structure across the trivial and topological regimes. After synthesizing Bi_1-xSb_x/Permalloy heterostructures in vacuo with a clean interface, we use spin-torque ferromagnetic resonance (ST-FMR) measurements at room temperature to study the SOT as a function of alloy composition. The experimentally observed behavior of charge-to-spin conversion in Bi_1-xSb_x is then compared to theoretical calculations of the spin Hall conductivity in this material system Phys. Rev. Lett. 114, 107201 (2015). Supported by the Penn State 2DCC-MIP under NSF Grant No. DMR-2039351 and by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by the National Institute of Standards and Technology (NIST).