To rotate photos, you must be logged in. From the Photo Tools Menu, choose Rotate Photos.
The following will appear:

Simply click each photo you want to rotate. They will be highlighted in red.
Then choose the direction you would like to rotate them — right, down, or left — and click the rotate button.
Rotation will occur in the background and may take several minutes. In the meantime, you can continue to use SmugMug. As you browse your gallery or click refresh while viewing it, your newly rotated photos will gradually replace those that are currently there.