How long does it take asteroids to orbit the Sun? 

There are asteroids peppering the Solar System everywhere, so it's impossible to give a precise answer to your question.

However, there are three main concentrations of asteroids within the Solar System:

• The Asteroid Belt - this sits in orbit between Mars and Jupiter. So far, more than 7,000 asteroids have been discovered within this belt, with more being discovered every year.
• The Kuiper Belt - this orbits the Sun just beyond the orbit of Neptune (the farthest planet from the Sun). It consists of lots of small, icy bodies. Its proximity to Neptune means that many objects are knocked out of orbit by collisions with this planet.
• The Oort Cloud - there is no direct evidence that this actually exists, because the asteroids are so small and these theoretical bodies are a very long way away. One estimate suggests there may be as many as one trillion asteroids within the Oort Cloud

I can't possibly tell you how long each asteroid takes to orbit the sun, because there are far too many. But there are some notable bodies, whose orbitary periods will at least help to give a rough answer to your question.

Ceres, the largest known asteroid in the Solar System, sits within the Asteroid Belt and has an orbital period of 4.6 years.

2060 Chiron is a minor planet, which has an orbital period of 50.7 years. Its orbit sits between Saturn and Uranus, and it belongs to a family of small astronomical bodies known as Centaurs, which all have unstable orbits.

Pluto is a dwarf planet whose orbit sits within the Kuiper Belt. It is the second-largest dwarf planet in the Solar System, after Ceres. It has an orbital period of 246 years, which gives you some indication of the orbital periods of other asteroids out there in the Kuiper Belt territory.