Bad idea. There is no physical barrier keeping a cigarette from entering the mouth. However, if an asthmatic wants to constantly be reminded what an asthma attack feels like, then a cigarette would achieve this goal. If minimizing symptoms is the goal, then any smoking...Tobacco, marijuana, second-hand, e-cigarette, cocaine, meth, etc., should be avoided.
Should not... An asthma patient can smoke but it will likely worsen symptoms, increase number/severity of exacerbations as well as increasing risk of copd, lung cancer, other types of cancer, etc. Smoking is unhealthy for everyone, including asthmatics. Smoking cessation can be done so see your doctor for advice and help.
Not safely. It is only a good idea for an asthmatic to smoke if that patient doesn't mind risking a life threatening asthma attack.
You can... ...technically speaking, but you shouldn't. Not only does cigarette smoke damage your lungs, but they reduce the efficacy of the medications we'd use to treat an asthma attack. So actually, no, you cannot smoke.