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Varies by creditor and card type. Amex allows as young as 15 on some cards
Google "The Master Minimum Age for Authorized Users Thread"
Unless I'm mistaken, most banks don't care. My wife and I are AUs on each others cards and often they only ask for a name. Occasionally an SSN. But as far as I can remember, only Amex asks for a DOB and restricts it to >=15.
In Amex's case, they are also fairly unique in which each AU (or ACM as the case may be) get's their own sub-account with a unique card number. It also establishes a new profile for that person. Most of the time with other banks, the AU card is identical in every way except for the name printed on it, and the primary account holder (and joint ones if applicable) hold all the responsibility.