Can chemotherapy cause a stroke?

Yes (but most don't) While cancer is a hypercoagulable state and can increase your risk for stroke, i know of one chemotherapy agent (there may be more, but it is quite uncommon) that can cause stroke. Asparaginase, used to treat certain leukemias, can cause strokes.
In theory, . Patients with cancer and patients on chemo have a higher risk for thrombotic (clotting) events. I would say the answer to your question is: possibly, especially in patients who already have higher risk for stroke like those with smoking history, cardiovascular disease, high blood pressure, etc.