We investigate the use of a split-ring resonator (SRR) incorporated with an atomic-vapor cell to improve the sensitivity and the minimal detectable electric (E) field of Rydberg atom-based sensors. In this approach, a sub-wavelength SRR is placed around an atomic vapor-cell filled with cesium atoms for E-field measurements at 1.3 GHz. The SRR provides a factor of 100 in the enhancement of the E-field measurement sensitivity. Using electromagnetically induced transparency (EIT) with Aulter-Townes splitting, E-field measurements down to 5 mV/m are demonstrated with the SRR, while in the absence of the SRR, the minimal detectable field is 500 mV/m. We demonstrate that by combining EIT with a heterodyne Rydberg atom-based mixer approach, the SRR allows for a sensitivity of 5.5 μV/m Hz, which is two-orders of magnitude improvement in sensitivity than when the SRR is not used.