Can a brain tumor cause a chronic cough?

Yes ... But : A brain tumor can cause a chronic cough, but the chances of this happening are so remote that you don't need to worry about it. There are hundreds of causes of chronic cough more likely than a tumor. See your doctor and get cracking.

Very unlikely: It's natural, especially when you are young, to be concerned about the most frightening diseases. The chances that a cough is produced by a brain tumor without any other obvious symptoms is negligible, and you'd do much better to seek the real cause. Your physician's exam and perhaps a chest x-ray is your best start. Remember subtle asthma can present just with cough.