We present the 850 $\mu$m polarization observations toward the IC5146
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 (JCMT), as part of the B-fields In STar forming Regions
Observations (BISTRO). This work is aimed at revealing the magnetic field
morphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS)
located at the end of a parsec-scale filament. To investigate whether or not
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 (PDF) of the observed polarization fraction for low signal-to-noise
ratio (SNR) data. We find a power-law dependence between the polarization
fraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 mag
regions, suggesting that the dust grains in these dense regions can still be
aligned with magnetic fields in the IC5146 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$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi
method, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ and
an Alfvénic Mach number of $<$0.6. These results suggest that gravity and
magnetic field is currently of comparable importance in the HFS, and turbulence
is less important.