To find the right tool panel in Photoshop:
For Photoshop CS5 and lower, access the animation window by opening “Window” + “Animation.” Likewise, click “Window” + “Timeline” in Photoshop CS6 and Photoshop CC to access the Timeline window. For Photoshop CC, click the drop-down menu in the middle of the Timeline window and select “Create Frame Animation.”
Then, one method would be having each frame of your animation in one separate layer. It means that, in your case, you should have the same object in all layers, but with different angle rotations applied to each of them.
To duplicate a layer:
Right click on the layer to see context menu, click on "Duplicate Layer".
To rotate an object:
With Photoshop you can select any object (you should select the right layer where the object is), right click on the object to see context menu, select "Transform" and you will be able to rotate the object manually (by dragging one corner) or writing the exact angle in the angle input on the top bar (it appears after you click on "transform").
In the Photoshop’s sequencing tool panel we activated before, click on small, right-facing arrow in the upper-right hand corner, and then select “Make Frames From Layers.”
The smoothness of the animation depends on how much frames you have and how fast do you show them. If you use 24 fps (Frames Per Second) or a higher value, no jumps between frames will be noticed by the viewer.
More info about animation smoothness: http://www.adobe.com/devnet/flash/learning_guide/animation/part02.html
Source and tutorial about animated gifs with Photoshop: http://www.digitaltrends.com/social-media/how-to-make-an-animated-gif