Does the Quran say the sun orbits the earth?

No

And it is He who created the night and the day and the sun and the moon; all [heavenly bodies] in an orbit are swimming.” Qur’an (21.33)

There is clearly no mention of the Sun orbiting the Earth. Just excuses.

But what it actually says is that the Sun is orbiting on its own orbit around the galaxy. Which science discovered quite recently.

Earth is floating/swimming. Science just proved it in year 2015/2016 that all the celestial bodies in the universe are floating/swimming on unseen fabric just as a ball float/swim on water.