No, this does not disqualify you, you're fine.  IF it was within 10 years ago when you fill out your SF-86 form for your security clearance, if you get to that point in the process, just report it.  If it was more than 10 years ago (like 10 years an one month), do not report it.  They only ask for criminal activity in the last 10 years, unless it was a felony then they ask for lifetime history.

I know plenty of people with misdemeanors and minor arrests and still have top secret clearance.  Time passed since the event is the key to mitigation, and ten years since your last arrests is more than enough time.