-- Updated -- : July 1st, 2016
Really does depend on the format in Adobe ® Photoshop ®. If the object is a layer or fill (pixels) and if it is on a layer. You can see the current state of the work via the layers panel (accessed via the window menu). If you are looking for sets of the artworks for use with the CSH and cookie cutter tool then there are 3D custom shapes for use with PS and PS Elements as well as abstract custom shapes etc
If the graphic is applied as a fill and it is applied to a layer then you can quickly rotate the layer by selecting the layer (in the layer panel) and then go to the edit menu and transform and rotate command. You can then either enter a value in the top bar options for the rotation (rotate text filed) or you can just use the art bounds controls to manually rotate the custom shape layer in Adobe ® Photoshop ®. To finish, press enter or click the tick button. You can also use the transform command to repeat the rotation or set up a keyboard shortcut for the operation.
In this case, the custom shape can be rotated via the image menu command and image rotation where you can use on the defined rotations or set an arbitary rotation. You may find the image is re-sized and the background color is added to the new created background (you might like to set this beforehand via the toolbox)
You might like to set the show transform controls to ON (this can be found in the top bar options in Adobe ® Photoshop ® when using a shape layer). You can then use the art bound / transform controls to manually rotate the custom shape. When you start rotating the path using the transform controls in Adobe ® Photoshop ®, the rotation text box will appear along the top option bar and you can enter a new value for the rotation. You can also update the rotation by holding the mouse down and placing the mouse over the little rotate icon and drag the mouse left or right to decrease or increase the angle. Click the tick button or press return to complete both operations. Another way to rotate the PS layer is via the edit menu and transform command (and rotate). With CC, you can also apply various transforms to the rectangle and live shapes but for some weird reason, there is no rotation option.
You can also just select the item in Adobe ® Photoshop ® and then go to the edit menu and use the copy (or cut) command and then paste the path in Adobe AI and use the rotation features of Illustrator.
You can always use actions to capture a rotation. Select a custom shape and then goto the action panel and then select the new action command and record the various steps such as rotate by 45 degrees. Give a name to the action and this action can be used to rotate a selected custom shape by 45 degrees etc with a single click. Of course, you can setup a range of actions such as rotate by 1 degree or 5 degrees etc and these can be applied over and over in seconds. A very quick and useful way to rotate a custom shape in Adobe ® Photoshop ®.
Once you have transformed the path in Adobe ® Photoshop ®, you can always go to the edit menu and use the define command to save the work for future use or save it to the CC library
One additional oversight (I think) with the rotation of custom shapes is that the comp / layer comp feature preserves the various states of position but does not preserve rotation. So if you create a custom shape layer and then save a layer comp (#ia the layer comp panel) and then rotate it and save that, the layer comp does not include that information.
A quick youtube video showing a few ways to do the task. The video is by Andrew Buckle Rotating tutorial [Youtube]