Well, have they?
How perfect is perfect? I had a teacher once who was pretty good, and you could hold a cardboard circle up to his drawing and it would match. But as my grandfather would point out - standing next to the chalkboard will cause the gravitational force of your body to immeasurably pull at the chalk line, as well as the board, so nothing is ever “perfect” in reality.
I’ve always heard a legend that Michaelangelo did.
Supposedly after he was chosen to paint the Cistine Chapel, there was a lot of political in-fighting. Some of the powers that be (well, were, anyway) insisted that they “audition” other artists. Michaelangelo was asked to submit a drawing along with the others. Insulted, he went in, laid a piece of paper on a desk and drew a perfect circle. He wordlessly handed them the paper and stormed out, knowing that anyone who knew anything about drawing would be vastly impressed and those who didn’t undertstand the significance would have their ignorance exposed.
Probably apocryphal, but it’s the only story I’ve ever heard of someone drawing a perfect circle free-hand.
Don’t know about drawing one but I knew a fellow who was “one.” 
To paraphrase WhyNot, how fine do you want to split the hairs? A perfect circle is a collection of points all of which are at the same distance from another point called the center of the circle. A point is just a location and has no physical size and no one can draw a point. So no one can draw a perfect dircle.
Is that a fine enough hair split?
It’s an old art-historical trope, popular since Pliny or so. Apelles could do it (according to Pliny); riffing off that Vasari (a good Classically-educated humanist type) says Giotto could do it, etc.; afterwards this gets shuffled over to the better-known Michelangelo by tour guides or something. Just a standard commonplace legend, and I would wager ALWAYS apocryphal. Sure, someone could probably do something close, but these stories like “the Pope asked for proof of his ability so he nonchallantly blah blah” are rote.
Right, but without splitting hairs the question does make sense in a practical way. i.e. *Can someone draw a circle free-hand that would be indistinguishable (visually) from a circle drawn with a fixed-radius tool. *
Apparently Michaelangelo is a contender.
Sure. I can do a pretty good job of it. So can you with a little practice. For example, hold two pencils chopstick-style, and rotate the paper using one pencil point as a pivot, and you’re essentially a human compass. If you’re only allowed one pencil (because the second one is a “tool”), use a fingernail as a pivot
There are many other distinct techniques, some more “freehand” than others. I suppose you could use them to win bar bets.
Is this really that hard for someone that works at it? I had a friend in HighSchool who was an aspiring artist and put a lot of time into practicing drawing and painting. She could draw a circle freehand which looked to me about as good as I could do with a compass, and while I thought it was a mildly impressive trick, figured that it was something just about anyone who had some ability and put a lot of time into sketching things could do.
Course if I actually measured it with a compass, I’m sure I could find imperfections, but visually it looked fine.
The characters in FullMetal Alchemist do it all the time. Heck, some of those circles are as big as rooms! 
It is hard, for a number of reasons; chiefly, the mechanical construction of the human arm and hand makes it quite easy to draw arcs that are convex with respect to the elbow or wrist, but hard to draw arcs that are concave to it.
Also, it’s quite easy for our perception to accept as circular an ellipse that is a bit wider than it is tall; comparing height to width purely by eye ius actually quite tricky (and many optical illusions make good use of this) - this phenomenon was driven home to me when I got a flat panel monitor that swivels so that it can be viewed in portrait format - the first time I used it that way, it seemed much taller than it had been wide and much narrower than it had been tall - in other words, my perception of the whole aspect ratio was messed up.
That’s not to say that a skilled artist couldn’t work hard to attentuate these problems, but they shouldn’t be underestimated.
Perfect circles exist only in the imagination.