Not long after I was told. Unfortunately, I was told when I was in my early twenties, after I'd already "done time" in the mental ward, by a psychiatrist with an AS son who caught what my mom had been trying to hide all my childhood. That was the beginning of good things for me; knowing how I was different made it so much easier to learn what I needed. If you don't know why you're different, you blame it on yourself; you take all the labels that others give you, like stupid and lazy and immature... It's so much easier to know.
Your son's an individual. When he accepts it depends on a lot of factors. Knowing for absolute sure that you love him, including loving his autism, helps a great deal. So does knowing that his problems are solvable, that his differences are acceptable, that disability is not inherently negative.
I think, if I had it to do over again, I would probably tell people. I'm very afraid of hurting people accidentally by saying the wrong thing; and them knowing I'm autistic would mean it would be easier to explain, and be believed, when I said that I hadn't been aware that I had been saying or doing something they interpreted as unkind. As it was, I didn't interact much in middle school (or in high school; I made my first friends in college); so I don't know that it would have changed all that much to tell people.
But it is his choice; don't make it for him. The more he learns that he should make his own decisions, determine his own life, the better. I know; he's a teenager; and maybe that's scary to you; but in my experience, kids growing up with disabilities get hit from all sides by the idea that they're incompetent to decide for themselves, when they very clearly aren't. These are the years when he's learning what he needs to know to go out into the world on his own. Learning what works for him as far as explaining his disability, and what doesn't, is an important task during this time. At his age, I wasn't thinking yet about what other people thought of me; as I said, I remained oblivious for quite a long time; but evidently he seems to be thinking about it, and is aware of the prejudice often leveled at those who are different. Hiding the difference is one option; but after a while, it really starts to become exhausting. It's no wonder that a lot of us use "coming out of the closet" as a synonym for disclosing autism to friends or co-workers.
Disability, strictly, only needs to be disclosed when there's a need for an accommodation. In your son's case, that'll probably be at school and later at college or at work. But there are times when talking about it can make it better; and times when it can make things worse. In general, the more people are open and honest about their own invisible disabilities, the more people will be exposed to them as acceptable variations, and the better things will get for all of us. But we are still at the stage where those first few, though they'll get the rewards of not having to hide, will still be facing prejudice.