International audienceWe experimentally analyze the shape of a long elastic filament rotating in a viscous liquid. We identify a continuous but sharp transition from a straight to an helical shape, resulting from the competition between viscous stresses and elastic forces. This induced helicity generates a propulsive force along the axis of rotation. In addition, we show that the shape transition is associated with an unstable branch in the force-torque relation, confirming the numerical predictions of Manghi et al. [Phys. Rev. Lett. 96, 068101 (2006)]. A linearized model of the fluid-structure interaction is proposed to account for all the features of the nonlinear filament dynamics