You can still use Initial Mesh Orientation and then feed a Random Range Float for the angle.
In the example below I’ve set the “Mesh Orientation Mode” to “Orient to Quaternion”, then used a “Make Quat from Axis Angle” as the input and a “Random Range Float” between 0 and 360 for the “AngleInDegrees”
Of course, I also had to change the particles’ “Facing Mode” to “Camera Position”
You could also bake down the circular blood mesh to a texture so that you can use a sprite instead of the static mesh in your emitter. But you probably have your reasons to have it as a static mesh