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We report 850~$\mu$m dust polarization observations of a low-mass ($\sim$12$M_{\odot}$) starless core in the $\rho$ Ophiuchus cloud, Ophiuchus C, madewith the POL-2 instrument on the James Clerk Maxwell Telescope (JCMT) as partof the JCMT B-fields In STar-forming Region Observations (BISTRO) survey. Wedetect an ordered magnetic field projected on the plane of sky in the starlesscore. The magnetic field across the $\sim$0.1~pc core shows a predominantnortheast-southwest orientation centering between $\sim$40$^\circ$ to$\sim$100$^\circ$, indicating that the field in the core is well aligned withthe magnetic field in lower-density regions of the cloud probed bynear-infrared observations and also the cloud-scale magnetic field traced byPlanck observations. The polarization percentage ($P$) decreases with anincreasing total intensity ($I$) with a power-law index of $-$1.03 $\pm$ 0.05.We estimate the plane-of-sky field strength ($B_{\mathrm{pos}}$) using modifiedDavis-Chandrasekhar-Fermi (DCF) methods based on structure function (SF),auto-correlation (ACF), and unsharp masking (UM) analyses. We find that theestimates from the SF, ACF, and UM methods yield strengths of 103 $\pm$ 46$\mu$G, 136 $\pm$ 69 $\mu$G, and 213 $\pm$ 115 $\mu$G, respectively. Ourcalculations suggest that the Ophiuchus C core is near magnetically critical orslightly magnetically supercritical (i.e. unstable to collapse). The totalmagnetic energy calculated from the SF method is comparable to the turbulentenergy in Ophiuchus C, while the ACF method and the UM method only set upperlimits for the total magnetic energy because of large uncertainties.

The JCMT BISTRO Survey: The Magnetic Field In The Starless Core $\rho$ Ophiuchus C