According to the high‐Tc superconducting bearing experiments, the magnetic flux‐drag torque due to the asymmetric magnetic field distribution of the magnet cannot be neglected. A homemade vertical torsion balance has been constructed to directly measure the flux‐drag torque acting on a yttrium‐barium‐copper‐oxide (YBCO) superconducting sample due to the off‐axis circular motion of a small permanent magnet. It is found that these flux‐drag torques, unlike the levitation forces, have no obvious hysteretic effect. Also, these flux‐drag torques are larger for a melt‐powder‐melt‐growth YBCO superconducting sample than for a ceramic YBCO sample.