JACO (Kinova Technology, Montreal, QC, Canada) is an assistive robotic manipulator that is gaining popularity for its ability to assist individuals with physical impairments in activities of daily living. To accommodate a wider range of user population especially those with severe physical limitations, alternative control methods need to be developed. In this paper, we presented a vision-based assistive robotic manipulation assistance algorithm (AROMA) for JACO, which uses a low-cost 3D depth sensing camera and an improved inverse kinematic algorithm to enable semi-autonomous or autonomous operation of the JACO. The benchtop tests on a series of grasping tasks showed that the AROMA was able to reliably determine target gripper poses. The success rates for the grasping tasks ranged from 85% to 100% for different objects.