A minimal model of cellular mechanosensing system that consists of a single stress fiber adhering on a substrate via two focal adhesions made of catch bonds is adopted to investigate the phenomena of cell reorientation on substrates induced by an applied uniaxial cyclic stretch. The model indicates that the catch bonds in the focal adhesions experience a periodically oscillating internal force with amplitude and frequency controlled by two intrinsic clocks of the stress fiber, one associated with localized activation and the other with homogeneous activation of sarcomere units along the stress fiber. It is shown that this oscillating force due to cyclic stretch tends to destabilize focal adhesions by reducing the lifetime of catch bonds. The resulting slide or relocation of focal adhesions then causes the associated stress fiber to shorten and rotate to configurations nearly perpendicular to the stretching direction. These predicted behaviors from our model are consistent with a wide range of experimental observations.