Depends. On the cause. Really there are few cures for anything in medicine, we just treat the symptoms. It might be something that one is exposed to that is causing the angioedema and by limiting that exposure it will stop the swelling.
Symptom not disease. Angioedema is a symptom of a variety of diseases. There is no panacea that treats all causes of angioedema. Angioedema may accompany hives. It may be a symptom of anaphylaxis. Aspirin, ibuprofen, antibiotics, & some blood pressure medications can cause angioedema. There are inherited disorders. Your pcp & board-certified allergist can help you with this. Cure depends on the cause.