Here’s one way you could do it:
* Key the random effector’s seed parameter. Then move the timeline to (for example) frame 10. Increase the seed parameter by 10, and key again;
* Select the random effector in the timeline and run Functions>Bake Object with only “Parameters” checked. Set the end time to frame 10;
* Select all the keys and set the interpolation type to Step;
* Scale the key selection to the length of your animation.