We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find α Na = 24.11(2) stat (18) sys × 10 −24 cm 3 , α K = 43.06 (14)(33), and α Rb = 47.24(12)(42). Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with 0.3% uncertainty. We find α Rb /α Na = 1.959(5), α K /α Na = 1.786(6), and α Rb /α K = 1.097(5). We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find α K = 43.06(21) and α Rb = 47.24(21).