  The torsion pendulum is a prevailing instrument for measuring small forces
acting on a solid body or those between solid bodies. While it offers powerful
advantages, the measurement precision suffers from thermal noises of the
suspending wires giving rise to stochastic torque noises. This letter proposes
a new scheme to reduce the effect of such noise by employing a double torsion
pendulum and cross-correlation technique based on the theoretical analysis that
the thermal torque noise appears at each end of the suspending wire
differentially. Cross-correlating two synthesized data streams which are
composed of the rotation angles of two torsion stages, it yields the power
spectral density estimate of external forces acting on the lower stage with the
reduced effect from the thermal torque noises. As an example use case, we
discuss the application to the study on the coupling strength of ultra light
dark matter to standard model particles. Our evaluation indicates that the
upper limit may be improved by an order of magnitude than the previous
experiments at 2 mHz, which corresponds to about $8\times10^{-18}$ eV.
