The deformability of red blood cells (RBCs) is an important property that allows the cells to squeeze through small capillary vessels and can be used as an indicator for disease. We present a microfluidic based technique to quantify the deformability of RBCs by stretching a collection of RBCs on a timescale of tens of microseconds in a microfluidic chamber. This confinement constrains the motion of the cell to the imaging plane of the microscope during a transient cavitation bubble event generated with a focused and pulsed laser. We record and analyze the shape recovery of the cells with a high-speed camera and obtain a power law in time, consistent with other dynamic rheological results of RBCs. The extracted exponents are used to characterize the elastic properties of the cells. We obtain statistically significant differences of the exponents between populations of untreated RBCs and RBCs treated with two different reagents: neuraminidase reduces the cell rigidity, while wheat germ agglutinin stiffens the cell confirming previous experiments. This cavitation based technique is a candidate for high-throughput screening of elastic cell properties because many cells can be probed simultaneously in situ, thus with no pre-treatment.