Qualifications
The first thing you'll need to become an EEOC officer is empathy and a strong desire for justice. If you prefer to just let things sort themselves out, you probably won't like this job much; it's not about letting the universe deliver karma at the appropriate time. It's about handing out that karma yourself. EEOC officers want the world to change, and they're not afraid to roll up their sleeves and "encourage" change to come a little bit faster.
The other thing you'll need is a bit more concrete: a college degree. Most EEOC officers have a bachelor's or master's degree (source) in a field like business administration or human resources. It's possible to land this job without either, but the odds aren't good. You could get lucky and land a position with an associate's degree and some on-the-job training, or you could get really lucky and get into this field by gaining experience in a related field.
Luck is a pretty scarce commodity these days, and the projected growth for this job is slightly slower than molasses in January (source). In the long run, it's easier and safer to get that four-year degree.