The "Born to Die" star is currently having construction work done on her beachfront Malibu pad, where a building worker came across the male trespasser, reported TMZ.
The man had allegedly turned the garage into a living space, but he had disappeared by the time authorities were called to the scene.
He left behind his laptop and various notes, which suggest he believed he had a "spiritual connection" with Rey, 30.
He is believed to have recently travelled to California from Kansas and has since been booked on a charge of felony burglary after allegedly stealing one of Rey's books.