  We perform magnetic susceptibility and magnetic torque measurements on the
organic $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Br, which is recently suggested to
host an exotic quantum dipole-liquid in its low-temperature insulating phase.
Below the metal-insulator transition temperature, the magnetic susceptibility
follows a Curie-Weiss law with a positive Curie-Weiss temperature, and a
particular $M\propto \sqrt{H}$ curve is observed. The emergent
ferromagnetically interacting spins amount to about 1/6 of the full spin moment
of localized charges. Taking account of the possible inhomogeneous
quasi-charge-order that forms a dipole-liquid, we construct a model of
antiferromagnetically interacting spin chains in two adjacent charge-ordered
domains, which are coupled via fluctuating charges on a Mott-dimer at the
boundary. We find that the charge fluctuations can draw a weak ferromagnetic
moment out of the spin singlet domains.
