I get asked this so much I thought I would make a guide I could point people to.

How to Rotate your Vendor
1. Stand on the ground below your vendor(s)

2. Double click your vendor you wish to turn and in the corresponding menu, choose, "See Goods"

3. Your vendor will pop down to where you are standing. Move your character to the direction you wish the vendor to be facing. In this case, my vendor is currently facing North, and I want him to face East.

4. Double Click your vendor again. On the corresponding menu choose, "Customize"

5. This will open another menu. Immediately right-click this menu to close it. This will turn your vendor to your directing. Then just return your vendor and they will continue facing the direction you have set.