Can i still be a police officer if i have asthma?

Yes: In general, the diagnosis of asthma should not limit you (except from possibly the military). Asthmatic patients should be able to do just about anything, including run marathons, if their asthma is under adequate control.

Depends: It depends on the local departments policy and probably depends on how well controlled the asthma is. Asthmatics can be surprisingly functional - che guevera had bad asthma during the cuban revolution well before there were real controller medicines available but he also almost died several times from the asthma.

Usually: Each agency can set standards of what they will accept based on their work environment, but as long as you are properly managed and can do strenuous exercise without more than rare need for your rescue inhaler, then should not be a problem.