The moon doesn't orbit the sun, or not directly. What happens is that the Earth orbits the sun and the moon orbits the earth. So it takes the moon just under 28 days (27.322 days to be exact) to make a full orbit of the earth. That's why we talk about the lunar month, which is 28 days and of which there are 13 in a year.
The earth, on the other hand, takes one day to rotate on its axis - that's how we get day and night - and about a year to orbit the sun - to be exact again, it takes 365.25 days. That's why every 4 years we have a leap year, with an extra day on 29 February, because after 4 years you end up with an extra day, and if you didn't add a day onto the calendar the dates would gradually get out of alignment with the earth's movement round the sun.