As JAKEZINC already said, you can rotate the emitter. Here are some examples of a global sequence that uses simple linear clockwise rotation:
Around the X axis
0: { 0, 0, 0, 1 }
200: { 0.707107, 0, 0, -0.707107 }
400: { -1, 0, 0, 0 }
600: { 0.707107, 0, 0, 0.707107 }
800: { 0, 0, 0, -1 }
Around the Y axis
0: { 0, 0, 0, 1 }
200: { 0, 0.707107, 0, -0.707107 }
400: { 0, -1, 0, 0 }
600: { 0, 0.707107, 0, 0.707107 }
800: { 0, 0, 0, -1 }
Around the Z axis (this is probably the one you need since the "surface" of the particle emitter is always initially parallel to the XY grid)
0: { 0, 0, 0, 1 }
200: { 0, 0, 0.707107, -0.707107 }
400: { 0, 0, -1, 0 }
600: { 0, 0, 0.707107, 0.707107 }
800: { 0, 0, 0, -1 }
Rotation in the examples above looks like this:
0 - 0 degrees
200 - 90 degrees
400 - 180 degrees
600 - 270 degrees
800 - 360/0 degrees
As you can see, rotations need to have a key every 90 degrees or less. These examples use a global sequence with a duration of 800 frames, but you should change it depending on how fast you want the emitter to rotate.