You CAN join the military with asthma, it just a matter of how severe it is. In example, someone like me who has exercise endused asthma, like when I run too much or do to much strenuous activities I have a greater chance of having an attack, I would be best avoiding joining the military. Though if your asthma is minor and you haven't had to use a fast acting inhaler or other asthma related medicine in few years, then go for it. As long as you can keep it under control without an inhaler or other medications your fine