You can even move an entire army formation that way too, as long as all units are grouped, either into one or more groupings.

Alt + drag left or right will rotate the selected formation around its centre point, or the entire army if you so desire. The same condition applies. This is incredibly useful for wheeling to face the whole army another direction if the enemy army happens to have entrenched itself on a hill at the corner, while preserving unit positions relative to one another. Warning though, if not all units are grouped and have a formation applied to them (e.g. single line etc) from the 8 choices available, if you try the alt advance with the entire army the AI will redeploy your army into one of its many quirky formations. I've seen entire cavalry wings cross the army's front to progress to their new positions before, when I left my general's unit ungrouped.