We measure the ionizing photon production efficiency (ξ_ion) of low-mass galaxies (10^7.8-10^9.8 M_⊙) at 1.4 < z < 2.7 to better understand the contribution of dwarf galaxies to the ionizing background and reionization. We target galaxies that are magnified by strong-lensing galaxy clusters and use Keck/MOSFIRE to measure nebular emission-line fluxes and Hubble Space Telescope to measure the rest-UV and rest-optical photometry. We present two methods of stacking. First, we take the average of the log of Hα-to-UV luminosity ratios (L_Hα/L_UV) of galaxies to determine the standard log(ξ_ion). Second, we take the logarithm of the total L_Hα over the total L_UV. We prefer the latter, as it provides the total ionizing UV luminosity density of galaxies when multiplied by the nonionizing UV luminosity density. log(ξ_ion) calculated from the second method is ∼0.2 dex higher than the first method. We do not find any strong dependence between log(ξ_ion) and stellar mass, far-UV magnitude (M_UV), or UV spectral slope (β). We report a value of log(ξ_ion) ∼ 25.47 ± 0.09 for our UV-complete sample ( $-22 {M}_{\mathrm{UV}} -17.3$ ) and ∼25.37 ± 0.11 for our mass-complete sample (7.8 < log(M_*) < 9.8). These values are consistent with measurements of more massive, more luminous galaxies in other high-redshift studies that use the same stacking technique. Our log(ξ_ion) is 0.2-0.3 dex higher than low-redshift galaxies of similar mass, indicating an evolution in the stellar properties, possibly due to metallicity or age. We also find a correlation between log(ξ_ion) and the equivalent widths of Hα and [O III] λ5007 fluxes, confirming that these equivalent widths can be used to estimate ξ_ion. ^* Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. This research is based on observations made with the NASA/ESA Hubble Space Telescope obtained from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs 12201, 12931, 13389, and 14209.