The refractive index of a biological tissue is required for investigating the tissue's optical properties. Efforts have been made to characterize the refractive indices of biological tissues at a single wavelength, but it is more convenient to know the Cauchy's coefficients, which provide refractive index over a wide range of wavelengths. We demonstrate a method to noninvasively provide the Cauchy's dispersion coefficients of biological tissues using a micro-optical coherence tomography. Using the short-frequency Fourier transforms, the relative optical thickness of the sample in the wavelength range of the broadband source was obtained from interferograms. The coefficients of the Cauchy's equation were estimated based on the wavelength-dependent sample thickness. We validated the proposed method using distilled water and fresh rat cornea ex vivo, and the experimental results were consistent with the reference data.