We demonstrate superconducting nanowire single-photon detectors (SNSPDs) based on a fractal design of the nanowires to reduce the polarization sensitivity of detection efficiency. We patterned niobium titanium nitride thin films into Peano curves with a linewidth of 100nm and integrated the nanowires with optical microcavities to enhance their optical absorption. At a base temperature of 2.6K, the fractal SNSPD exhibited a polarization-maximum device efficiency of 67% and a polarization-minimum device efficiency of 61% at a wavelength of 1550nm. Therefore, the polarization sensitivity, defined as their ratio, was 1.1, lower than the polarization sensitivity of the SNSPDs in the meander design. The reduced polarization sensitivity of the detector could be maintained for higher-order spatial modes in multimode optical fibers and could tolerate misalignment between the optical mode and the detector. This fractal design is applicable to both amorphous and polycrystalline materials that are commonly used for making SNSPDs.