Neurodegenerative diseases are linked with dysregulation of the integrated stress response (ISR), which coordinates cellular homeostasis during and after stress events. Cellular stress can arise from several sources, but there is significant disagreement about which stress might contribute to aging and neurodegeneration. Here, we leverage directed transdifferentiation of human fibroblasts into aged neurons to determine the source of ISR activation. We demonstrate that increased accumulation of cytoplasmic double-stranded RNA (dsRNA) activates the eIF2α kinase PKR, which in turn triggers the ISR in aged neurons and leads to sequestration of dsRNA in stress granules. Aged neurons accumulate endogenous mitochondria-derived dsRNA that directly binds to PKR. This mitochondrial dsRNA leaks through damaged mitochondrial membranes and forms cytoplasmic foci in aged neurons. Finally, we demonstrate that PKR inhibition leads to the cessation of stress, resumption of cellular translation, and restoration of RNA-binding protein expression. Together, our results identify a source of RNA stress that destabilizes aged neurons and may contribute to neurodegeneration.