Can thymoma cancer cause an irregular menstrual cycle?

Yes. Any significant medical illness can interfere with the "hypothalamic-pituitary-ovarian axis" - the organs controlling the hormones responsible for normal menstrual cycles. Specifically regarding cancer, some treatments (like chemotherapy) can also damage the eggs inside your ovaries. While most young women with cancer "recover" their cycles, you might want to discuss this concern with your ob/gyn.