Assistive robotic manipulators have the potential to improve the lives of people with motor impairments. They can enable individuals to perform activities such as pick-and-place tasks, opening doors, pushing buttons, and can even provide assistance in personal hygiene and feeding. However, robotic arms often have more degrees of freedom (DoF) than the dimensionality of their control interface, making them challenging to use - especially for those with impaired motor abilities. Our research focuses on enabling the control of high-DoF manipulators to motor-impaired individuals for performing daily tasks. We make use of an individual's residual motion capabilities, captured through a Body-Machine Interface (BMI), to generate control signals for the robotic arm. These low-dimensional controls are then utilized in a shared-control framework that shares control between the human user and robot autonomy. We evaluated the system by conducting a user study in which 6 participants performed 144 trials of a manipulation task using the BMI interface and the proposed shared-control framework. The 100% success rate on task performance demonstrates the effectiveness of the proposed system for individuals with motor impairments to control assistive robotic manipulators.