If you are not in the army already and want to enlist you can be rejected for appointment, enlistment, and induction if you have herpes genitalia and condyloma acuminatum, acute or chronic, not amenable to treatment. Such treatment must be given and demonstrated effective prior to accession. This is applicable to both men and women.
This means that you need to keep your genital herpes under control. My own interpretation of this is that you should have a doctor that you visit regularly and that doctor would probably prescribe suppressive treatment. That doctor is your way of demonstrating that you have the virus under control.
In some states, if you do not have an obvious outbreak and you pass the general exam, they might not even ask about genital herpes. But you should know that stress usually triggers outbreaks and training, camps and deployment are stressful; and you want to focus on the mission not on the itch 🙂
If you are an active military member already and then contract HSV-2, they will not discharge you.
So the best thing is first educate yourself, see your health professional, have them sign that you have been tested and educated, talk to a medical specialist at the recruiting, get copies of anything in regulations pertaining to and forms etc.