My answer is YES, if you believe you have taught your child how to be financially responsible. This is not an easy task - let's face it, most adults don't use credit cards properly, evidenced by the incredible level of credit card debt in our country.
But, let's change that and help our children do it the right way. You can establish some good rules for using a credit card and then choose credit cards that offer some advantage to cardholders.
Here's an article with some helpful suggestions: