This paper presents a new class of animatronic soft robots created by a desktop fabrication mechanism called additive folding. In this method, two-dimensional (2D) slices are threaded by multiple strings, accordion-folded by flexure hinges and finally stacked into a predefined three-dimensional (3D) structure. As the 3D assembly of the slices is controlled by embedded strings, it becomes an animatronic soft robot that moves like a biological creature and that shows life-like movements. We create a computational design algorithm that takes as input a desired 3D geometry of the robot, and that produces a 2D surface with built-in folds and string-based actuators. This paper describes the entire robot design process and demonstrates various animatronic motions, highlighting the vision of desktop fabrication technology and its potential applications in animatronics and robotic art.