Small amplitude oscillatory shear flow of a fibre suspended in a dilute polymer solution is considered. Averaged over a cycle of the shear flow, the nonlinear elasticity produces a mean angular velocity of the fibre proportional to the square of the amplitude of the shear flow. Over many cycles this produces a slow drift in the orientation of the fibre towards alignment with the flow direction, an orientation that minimises the fibre＇s effect on the rheology.