Maybe. If your kid is a RESPONSIBLE college student, it might make sense. There are a lot of good credit cards for college students and graduate students, ones that offer rewards and even ones that try to encourage good spending habits.
That said, if you're leery about the idea, especially because you think your kid is a financial disaster waiting to happen, that may be an argument for making them an authorized user instead. You'll be liable for your kid's spending either way, but you're more likely to be aware of what's happening if the overspending and money mismanagement is on your credit card and not theirs.