Shape memory polymer (SMP) is a type of functional materials that changes Young's modulus when heated above glass transition temperature (Tg). In this work, this property of SMP has been explored for the design and fabrication of a modular omni-directional joint with variable stiffness. When cascading a number of such joints, a variable stiffness hyper-redundant robotic arm can be built. The basic design of the variable stiffness joint is based on a ball joint where the ball is made of two materials: acrylonitrile butadiene styrene (ABS) and SMP, and the socket is made of only ABS material. When heated, the ball joint shows different resistive torques below and above the SMP's glass transition temperature Tg. Moreover, shape recovery property of SMP material above Tg guarantees the design with high repeatability. Both the ball and the socket are made by a 3D printing process fused deposition modeling (FDM). The FDM fabrication of SMP is made possible by a novel process control method in the FDM process. The ball joint's variable stiffness is tested by a number of experiments. Experimental results indicate distinct changes in resistive torques at different test temperatures. Using the proposed modular omni-directional ball joints, a variable stiffness hyper-redundant robotic arm is built.