Title is worded a bit misleadingly, it sounds like something from outer space causes earthquakes, but it's not the case:

[...] any substantial earthquakes linked to disturbances in the Earth’s dynamo flows would alter the magnetic field, thus impacting the path of primary cosmic radiation. The fallout of these alterations would be apparent in the changes in the counts of secondary cosmic ray particles recorded by ground-based detectors.

So as I understand, when an earthquake happens, it also disturbs the magnetic field of Earth, and you can measure this disturbance by measuring cosmic radiation.