Using spectra taken with the AAOmega spectrograph, we measure the radial velocities of over 100 stars, many of which are intermediate age carbon stars, in the direction of the dwarf irregular galaxy NGC 6822. Kinematic analysis suggests that the carbon stars in the sample are associated with NGC 6822, and estimates of its radial velocity and galactic rotation are made from a star-by-star analysis of its carbon star population. We calculate a heliocentric radial velocity for NGC 6822 of -51+/-3km/s and show that the population rotates with a mean rotation speed of 11.2+/-2.1km/s at a mean distance of 1.1kpc from the galactic centre, about a rotation axis with a position angle of 26{deg}+/-13{deg}, as projected on the sky. This is close to the rotation axis of the HI gas disc and suggests that NGC 6822 is not a polar ring galaxy, but is dynamically closer to a late-type galaxy. However, the rotation axis is not aligned with the minor axis of the AGB isodensity profiles and this remains a mystery.