In the present study, the magnetic field scaling on density, $|B| propto rho^{kappa}$, was revealed in a single starless core for the first time. The $kappa$ index of $0.78 pm 0.10$ was obtained toward the starless dense core FeSt 1-457 based on the analysis of the radial distribution of the polarization angle dispersion of background stars measured at the near-infrared wavelengths. The result prefers $kappa = 2/3$ for the case of isotropic contraction, and the difference of the observed value from $kappa = 1/2$ is 2.8 sigma. The distribution of the ratio of mass to magnetic flux was evaluated. FeSt 1-457 was found to be magnetically supercritical near the center ($lambda approx 2$), whereas nearly critical or slightly subcritical at the core boundary ($lambda approx 0.98$). Ambipolar-diffusion-regulated star formation models for the case of moderate magnetic field strength may explain the physical status of FeSt 1-457. The mass-to-flux ratio distribution for typical dense cores (critical Bonnor--Ebert sphere with central $lambda=2$ and $kappa=1/2$--$2/3$) was calculated and found to be magnetically critical/subcritical at the core edge, which indicates that typical dense cores are embedded in and evolve from magnetically critical/subcritical diffuse surrounding medium.
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