I'm going to say 13, but with restrictions.
Not every child reaches/passes through puberty at the same age, meaning not every child becomes an adult at the same age. While there might be an average age where they reach adulthood, there are still people who reach it before or after. When I was younger there were other people who were over six feet at age twelve, while some didn't even begin growing until they were nineteen. In my state, California, this meant that the prior group had to suffer for six years before being able to legally consent, while the former were essentially still children when they could consent.
That being said, after the child reaches 13, they shouldn't be allowed to consent until there's some sort of confirmation that they have reached puberty. Perhaps some sort of form the parents would need to fill out, or they'd have to go to a doctor to have it verified?