We demonstrate that 3T3 fibroblast cells can exhibit periodic shape oscillations following a loss of cell-substrate adhesion. The oscillatory behavior can last many hours at a constant frequency, and can be switched off and on using chemical agents. We show that the oscillation frequency increases with increasing acto-myosin contractility. The oscillations also cease when extracellular calcium is depleted or when a blocker of calcium channels is introduced. We propose a theoretical description of the oscillations based on an instability of the cortical actin layer. The cortical actin layer is described using the hydrodynamic theory of active gels. We assume that calcium enters the cell via mechanically gated channels and that an increase of the calcium density increases the acto-myosin contractility in the cortical layer. The theory provides a stability diagram for the actin cortical layer showing an oscillatory instability and gives a good description of the oscillation period. We also discuss the connections between these oscillations and other oscillations observed after depolymerization of the microtubules and with the formation of blebs.