Contact between an adherent cell and the extracellular matrix (ECM) promotes the recruitment of structural and signaling molecules to the cytoplasmic domain of integrins, which mediate cell adhesion, cell migration, and cell growth. It is unclear whether the intracellular recruitment of these cytoplasmic molecules enhances the affinity between the ECM and the extracellular domain of the cell surface receptors (integrins). Using soft microneedles coated with Arg-Gly-Asp (RGD) peptides, a sequence commonly shared by ECM proteins, we apply a localized ramp shear stress to the surface of a HeLa cell and measure the cell stiffness and the collective (or apparent) unbinding lifetime of its surface receptors to RGD. These measurements demonstrate that both cell stiffness and the collective cell surface receptor-RGD unbinding lifetime increase with the duration of the pre-shear cell-microneedle contact and with the rate of shear applied to the cell membrane. These parameters are also crucially dependent on the integrity of the actin filament network. Our results are consistent with a model of positive feedback signaling where RGD-mediated initial recruitment of cytoskeletal proteins to the cytoplasmic domain of integrins directly enhances the interaction between the extracellular domain of integrins and the RGD sequence of ECM molecules.