This thesis presents an upper limb robotic exoskeleton and a method for actively engaging stroke patients during robotic rehabilitation by incorporating the patient's intentions into the robot's control scheme. Robotic rehabilitation is effective for sensorimotor training of patients who have some residual movement in their impaired limbs, but those with severe impairment benefit less due to the difficulty in determining movement intent. Intent recognition is necessary for providing an appropriate level of robotic assistance. Through implementation of a non-invasive brain-machine interface (BMI) using electroencephalography (EEG), the patient's movement intent is transmitted to the MAHI Exo-II, an upper extremity robotic exoskeleton. This thesis first validates the exoskeleton as the proper choice for clinical implementation by assessing its dynamics and performance characteristics as compared to other state-of-the-art designs. Then, results of pre-clinical trials with the BMI are described, laying the foundation for improved robotic rehabilitation and a better understanding of neural plasticity.