We introduce a simple micro-fluidic device containing an actuated flexible membrane, which allows the viscoelastic characterization of cells in small volumes of suspension by loading them in compression and observing the cell deformation in time. From this experiment, we can determine the characteristic time constant of recovery of the cell. To validate the device, two cell types known to have different cytoskeletal structures, 3T3 fibroblasts and HL60 cells, are tested. They show a substantially different response in the device and can be clearly distinguished on the basis of the measured characteristic recovery time constant. Also, the effect of breaking down the actin network, a main mechanical component of the cytoskeleton, by a treatment with Cytochalasin D, results in a substantial increase of the measured characteristic recovery time constant. Experimental variations in loading force, loading time, and surface treatment of the device also influence the measured characteristic recovery time constant significantly. The device can therefore be used to distinguish between cells with different mechanical structure in a quantitative way, and makes it possible to study changes in the mechanical response due to cell treatments, changes in the cell's micro-environment, and mechanical loading conditions.