We present the 850 μm polarization observations toward the IC 5146 filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) and its associated polarimeter (POL-2), mounted on the James Clerk Maxwell Telescope, as part of the B-fields In STar forming Regions Observations. This work is aimed at revealing the magnetic field morphology within a core-scale (≲1.0 pc) hub-filament structure (HFS) located at the end of a parsec-scale filament. To investigate whether the observed polarization traces the magnetic field in the HFS, we analyze the dependence between the observed polarization fraction and total intensity using a Bayesian approach with the polarization fraction described by the Rice likelihood function, which can correctly describe the probability density function of the observed polarization fraction for low signal-to-noise ratio data. We find a power-law dependence between the polarization fraction and total intensity with an index of 0.56 in A V ∼ 20-300 mag regions, suggesting that the dust grains in these dense regions can still be aligned with magnetic fields in the IC 5146 regions. Our polarization maps reveal a curved magnetic field, possibly dragged by the contraction along the parsec-scale filament. We further obtain a magnetic field strength of 0.5 ±; 0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi method, corresponding to a mass-to-flux criticality of ∼1.3 ±; 0.4 and an Alfvénic Mach number of <0.6. These results suggest that gravity and magnetic field are currently of comparable importance in the HFS and that turbulence is less important.