Can I join the us airforce with mild asthma?

If the diagnosis is. Wrong --- if you have asthma it would be worth making sure you really have asthma. Many people diagnosed with asthma don't really have it. An evaluation by a pulmonary md who knows you really need to know can clarify this using a bronchoprovocation challenge test.
No. The us armed forces list asthma as a reason for exclusion from service.