A polarization-insensitive, square split-ring resonator (SSRR) is simulated and experimented. By investigating the influence of the asymmetrical arm width in typical SSRRs, we find that the variation of the arm width enables a blue shift of the resonance frequency for the 0° polarized wave and a red shift of the resonance frequency for the 90° polarized wave. Thus, the resonance frequency for the 0° polarized wave and the resonance frequency for the 90° polarized wave will be identical by asymmetrically adjusting the arm width of the SSRR. Two modified, split-ring resonators (MSRRs) that are insensitive to the polarization with asymmetrical arm widths are designed, fabricated, and tested. Excellent agreement between the simulations and experiments for the MSRRs demonstrates the polarization insensitivity with asymmetrical arm widths. This work opens new opportunities for the investigation of polarization-insensitive, split-ring resonator metamaterials and will broaden the applications of split-ring resonators in various terahertz devices.