Mechano-sensation of cells is an important prerequisite for cellular function, e.g. in the context of cell migration, tissue organisation and morphogenesis. An important mechano-chemical-transducer is the actin cytoskeleton. In fact, previous studies have shown that actin cross-linkers, such as α-actinin-4, exhibit mechanosensitive properties in its binding dynamics to actin polymers. However, to date, a quantitative analysis of tension-dependent binding dynamics in live cells is lacking. Here, we present a new technique that allows to quantitatively characterize the dependence of cross-linking lifetime of actin cross-linkers on mechanical tension in the actin cortex of live cells. We use an approach that combines parallel plate confinement of round cells, fluorescence recovery after photo-bleaching, and a mathematical mean-field model of cross-linker binding. We apply our approach to the actin cross-linker α-actinin-4 and show that the cross-linking time of α-actinin-4 homodimers increases approximately twofold within the cellular range of cortical mechanical tension rendering α-actinin-4 a catch bond in physiological tension ranges.