Robotic devices can be leveraged to raise the abilities of humans to perform demanding and complex tasks with less effort. Although the first priority of such human-robot interaction (HRI) is safety, robotic devices must also be intuitive and efficient in order to be adopted by a broad range of users. One challenge in the control of such assistive robots is the management of the end-effector orientation, that is not always intuitive for the human operator, especially for neophytes. This paper presents a novel orientation control algorithm designed for robotic arms in the context of HRI. This paper aims at making the control of the robot's orientation easier and more intuitive for the user, both in the fields of rehabilitation (in particular individuals living with upper limb disabilities) and industrial robotics. The performance and intuitiveness of the proposed orientation control algorithm is assessed and improved through two experiments with a JACO assistive robot with 25 able-bodied subjects, an online survey with 117 respondents via the Amazon Mechanical Turk and through two experiments with a UR5 industrial robot with 12 able-bodied subjects.