A rotary screen door assembly for a work vehicle includes a door configured to couple to an enclosure of the work vehicle for movement between a closed position and an open position, and a screen rotatably supported on the door and configured to filter air passing through an air inlet defined in the door. The rotary screen door assembly also includes a first shaft segment rotatably supported on the door and coupled to the screen, the first shaft segment having a first magnetic coupler configured to engage a corresponding second magnetic coupler of the work vehicle.