Is there such thing as appendix cancer?

Yes: But they are rare - but not impossible.

Yes: Appendiceal cancers represent less than 2% of intestinal cancers. The most common type is a carcinoid tumor, often found incidentally after appendicitis. These are usually cured by appendectomy, sometimes requiring re-operation to remove a little more intestine and lymph nodes. More aggressive adenocarcinomas may be difficult to diagnose and can cause appendicitis.

Yes: The most common type of appendix tumor is a carcinoid tumor. Many of these are discovered by accident if someone has an appendectomy for appendicitis. If it has not spread or come from a distant source, removing all of it is curative. For other types, see nice summary at: http://www.Cancer.Net/cancer-types/appendix-cancer.