Proper orientation of the mitotic spindle plays a crucial role in embryos, during tissue development, and in adults, where it functions to dissipate mechanical stress to maintain tissue integrity and homeostasis. While mitotic spindles have been shown to reorient in response to external mechanical stresses, the subcellular cues that mediate spindle reorientation remain unclear. Here, we used a combination of optogenetics and computational modeling to investigate how mitotic spindles respond to inhomogeneous tension within the actomyosin cortex. Strikingly, we found that the optogenetic activation of RhoA only influences spindle orientation when it is induced at both poles of the cell. Under these conditions, the sudden local increase in cortical tension induced by RhoA activation reduces pulling forces exerted by cortical regulators on astral microtubules. This leads to a perturbation of the balance of torques exerted on the spindle, which causes it to rotate. Thus, spindle rotation in response to mechanical stress is an emergent phenomenon arising from the interaction between the spindle positioning machinery and the cell cortex.