Yes, you can join army even if you wear glasses. In fact, you are not required to have perfect vision in the military. There are lots of people in the army wear glasses. I heard that as long as you can be corrected to 20/20 vision, you can join the arm. If not, don't worry, you can ask help of Lasik surgery if you really want to join army. It will reshape your cornea that to recover your vision.
Of course, you can join the army even if you wear glasses. There are many people who wear glasses are in the army. Perfect vision is only required for certain positions. As long as your vision can be corrected to 20/20 vision with corrective glasses or contact lenses, you can join the army. So you don't have to worry about this. I have a friend who wear glasses, too. And now he is in the army.