There are non-driver photo identification cards available for people of any age, including children, from state departments of motor vehicles. A child must be accompanied by a legal guardian who can provide proof of the child's identity with a birth certificate.
If a child cannot sign his own name, that fact is indicated on the identification card by the DMV. There is normally a small service fee for the issuance of a state ID card. Other types of unofficial ID cards are available for purchase online through websites such as KidsTravelCard.com or EasyIDCard.com. In some cases, these sites are more expensive than an official picture ID card from the DMV.