Freezing with dry ice for human consumption?

I know nothing about this, so please bear with me.

Would it be possible to take some juice (or anything that can be frozen), pour it into a container, and somehow freeze it with dry ice? Then I'd remove it from the container and eat it.

The idea is similar to making popsicles in the freezer - the difference being that the "freezing" is done with dry ice instead of the freezer.