do you want to rotate a single led, or have multiple leds in a circle, where only one led is on, and progressively the next one is turned on? If so, how many leds?
I have three red ones, an orange, a yellow, a blue and a green LED Chaser.
They run for months on two or four AA alkaline battery cells and are very bright.
Instead of an LED always turned on, the LEDs blink for a moment then after chasing around a few times there is a pause. Then the average battery current is very low.
The LEDs are in a circle mounted on a CD.
At night the blue and green ones light up car reflective licence plates pretty far away.