Primary cilia are ubiquitous, microtubule-based organelles that play diverse roles in sensory transduction in many eukaryotic cells. They interrogate the cellular environment through chemosensing, osmosensing, and mechanosensing using receptors and ion channels in the ciliary membrane. Little is known about the mechanical and structural properties of the cilium and how these properties contribute to ciliary perception. We probed the mechanical responses of primary cilia from kidney epithelial cells [Madin-Darby canine kidney-II (MDCK-II)], which sense fluid flow in renal ducts. We found that, on manipulation with an optical trap, cilia deflect by bending along their length and pivoting around an effective hinge located below the basal body. The calculated bending rigidity indicates weak microtubule doublet coupling. Primary cilia of MDCK cells lack interdoublet dynein motors. Nevertheless, we found that the organelles display active motility. 3D tracking showed correlated fluctuations of the cilium and basal body. These angular movements seemed random but were dependent on ATP and cytoplasmic myosin-II in the cell cortex. We conclude that force generation by the actin cytoskeleton surrounding the basal body results in active ciliary movement. We speculate that actin-driven ciliary movement might tune and calibrate ciliary sensory functions.