Mathematica distinguishes between "Images" and "Graphics". See the documentation for information about them.
ImageRotate is for Images, but SphericalPlot3D produces a Graphic.
There is a specific function for Graphics rotation: https://reference.wolfram.com/language/ref/Rotate.html
Rotate[a, Pi/2, {0, 0, 1}]
Another way to do this is to use the ViewPoint option: http://reference.wolfram.com/language/ref/ViewPoint.html
Thanks for the reply Sean!
As mentioned above, I did also try the "Rotate" function as such:
Rotate[a,Pi/3,{1,0,0}]
And I got the error:
Coordinate {1, 0, 0} should be a pair of numbers, or a Scaled or Offset form.
Any idea why?
Thanks!