You may or may not have a problem. There are no US laws or regulations about using a box as carry on luggage. TSA shouldn't have a problem* and everything should be fine, as far as rules go.
That being said you have two potential issues that you need to watch for. The airline may have rules against it. Not laws or regulations, but just rules. Most airlines follow the same basic rules, so that travelers don't get confused, but there are some differences. Specially on budget airlines (where they may charge per carry on) or "high end" airlines where they want to discourage larger carry ons. So make sure to check with your airline directly.
*The second problem is going to be "it's unusual". Around holidays and throughout the year people carry boxes with gifts quite a bit, so this shouldn't be a problem, but every time you do something different then the norm, be prepared for someone else to have a problem with it. TSA people might take an extra through look, for example, or have to call their manager or some such. Make sure to leave some extra time for that non-sense.
So to be clear, you should not have a problem at the airport, the airline may have a rule against it, but that would be unusual and it's best to call them to find out.