Recently, soft actuator-based exosuits have gained interest, due to their high strength-to-weight ratio, inherent safety, and low cost. We present a novel wrist exosuit actuated by fabric pneumatic artificial muscles that can move the wrist in flexion/extension and ulnar/radial deviation. We derive a model representing the torque exerted by the exosuit and introduce a model-based optimization methodology for the selection of placement parameters of the exosuit muscles. We evaluate the accuracy of the model by measuring the exosuit torques throughout the full range of wrist flexion/extension. When accounting for the displacement of the mounting points, the model predicts the exosuit torque with a mean absolute error of 0.279 Nm, which is 26.1% of the average measured torque. To explore the capabilities of the exosuit to move the human body, we measure its range of motion on a passive human wrist; the exosuit is able to achieve 55.0% of the active biological range in flexion, 69.1% in extension, 68.6% in ulnar deviation, and 68.4% in radial deviation. Finally, we demonstrate the device controlling the passive human wrist to move to a desired orientation in the flexion/extension plane and along a two-degree-of-freedom trajectory.