Surfactant-mediated interactions acting along the line of shortest contact between carbon nanotubes have been investigated by many authors, but the surfactant-mediated torsion that arises in the case of angled tubes have so far been ignored. Here we show for the first time that a strong torsional force originates from the central surfactant aggregate that forms at the crossing between nonparallel nanotubes. Our dissipative particle dynamics simulations demonstrate that this torque pulls the tubes into a parallel arrangement. The torque increases strongly with decreasing angle between the tubes. This trend is due to the growth of the central aggregate which not only provides more molecules able to mediate the force but also increases the "lever arm" on which the force acts. Together with the strong surfactant-mediated attraction acting along the line of shortest contact between the tubes, the torsion increases the difficulty of nanotube dispersion, but could have a positive effect on carbon nanotube materials in which the adsorbed surfactant micelles are intended to bind the tubes together.