You ask for a day off, and you make it clear that you'll make up for that day off. If you can take half a day off rather than a full day off, you'll be even less disruptive.
As an intern, it's unlikely that what what you are working on is on a project's critical path - if you are on a critical path, then your boss should have known better than let the outcome of a project depend on an intern's contributions. Not very ego enhancing to you, but that's how I would have handled you as my intern - I don't want you to be to my team as a Chaos Monkey would be to Cloud operations. Nothing personal, but I have deadlines to meet, a team's reputation to preserve and managerial headaches I want to avoid.
Some interns have complained on this site that they were not 100% busy and in fact, that they were only 40% busy. If you fall into this category of interns, you'll make up for any time you take off very easily.
Your internship could end at your manager's whim. Further, you're not guaranteed that your manager will call you back once your internship ends. This means that you have to be proactive about your internship ending and being proactive means that you have to go on interviews.
In my time, I used to ask for some time off and I would have been very up front if the management asked me what I was up to - I would have told them that since they can't guarantee that they'll call me back, I have to have a plan B in place. They never asked because they had a pretty good idea why I was asking for the time off, and that my asking for time off was my being simply prudent about how I managed my future.