Boron arsenide (c-BAs) is at the forefront of research on ultrahigh thermal conductivity materials. We present a Raman scattering study of isotopically tailored cubic boron arsenide single crystals for 11 isotopic compositions spanning the range from nearly pure c-$^{10}$BAs to nearly pure c-$^{11}$BAs. Our results provide insights on the effects of strong mass disorder on optical phonons and the appearance of two-mode behavior in the Raman spectra of mixed crystals. Strong isotope disorder also relaxes the one-phonon Raman selection rules, resulting in disorder-activated Raman scattering by acoustic phonons.