Soft robots may potentially be used for human services and complex environmental locomotion. The bodies of the soft robots are made from soft materials to make them safe human interaction, and to enable them to deform enough to adapt to soft or rough terrains. However, their practical applications are limited because their body stiffness is too low and the deformation is continuous, which makes it difficult to control their movement. Here we report the design and implementation of a soft robotic arm driven by shape memory alloy (SMA) coils. The arm is made from soft silicone, and there are three linear Hall sensors in certain slots on the body wall to measure their changes in height as the arm bends. With a compression compensation algorithm, a PID controller is used to precisely control the bending movement. This soft robotic arm can follow a two-dimensional motion with a relatively high accuracy; indeed it displays quite a remarkable performance considering its low-cost, simple structure, easy control, and small bending error. Since this soft arm can be used as the basic driving unit of a soft robot capable of manipulating and locomoting, it has shed light on the applications of SMA soft robots.