Here's a picture online that I looked at for guidance.

I read online that the track measured 621 m (2,037 ft) in length and 150 m (387 ft) in breadth. I figured one minecraft block was maybe 3' x 3', so that would mean my copy would need to be about 679 blocks long and 129 blocks wide. I tried measuring this out, and it turned out to be a vast area that would require me to level 3 or 4 mountains. So I used dynamite to do this.
With a cross-sectional diagram I found online, I started with making a set of the stadium seats. I figured that once I had the pattern down, it would be fairly easy just to repeat it over and over to make the long sections down the sides. Here is what I ended up doing with the seats...



Next I built the gatehouses/gates where the chariots would have entered at the start of the race. I built one side and then copied what I had made to make the other side. Too bad I couldn't replicate the curve of the original.




Prepping the field is going to be very time-consuming...