The dark matter halos that surround Milky Way-like galaxies in cosmological simulations are, to first order, triaxial. Such halos are predicted to exhibit steady figure rotation with a median pattern speed 0.15h km/s/kpc ~ 0.15h radian/Gyr. The pattern speeds predicted by cosmological CDM simulations are so small that it is largely unimportant for galaxy evolution and very difficult to detect. We present a new way to detect figure rotation in the Milky Way halo using the morphology and 3-D velocities of stars in tidal streams, such as the kinematical data that are being obtained by Gaia and large multi-fiber spectroscopic Milky Way surveys like DESI. We show using simulations of a Sagittarius-like polar tidal stream in triaxial dark matter halos with different shapes that when the halos are rotated about one of the three principal axes, figure rotation produces warps and misalignments of the planes of the leading and trailing arms of the stream. For pattern speeds typical of cosmological halos we demonstrate, for the first time, that a Sagittarius-like tidal stream would be altered to a degree that is detectable with current observations. We also quantify the effects of figure rotation on the observed kinematics of thinner and shorter tidal streams. This discovery will potentially allow for a future measurement of figure rotation of the Milky Way’s dark halo, perhaps enabling the first evidence of this relatively unexplored prediction of CDM. This work is funded in part by NASA grants NNX15AK79G and 80NSSC20K0509 and a MICDE Catalyst Grant.