In this study, we present a tensegrity robot arm that can reproduce the features of complex musculoskeletal structures, and can bend like a continuum manipulator. In particular, we propose a design method for an arm-type tensegrity robot that has a long shape in one direction, and can be deformed like a continuum manipulator. This method is based on the idea of utilizing simple and flexible strict tensegrity modules, and connecting them recursively so that they remain strict tensegrity even after being connected. The tensegrity obtained by this method strongly resists compressive forces in the longitudinal direction, but is flexible in the bending direction. Therefore, the changes in stiffness owing to internal forces, such as in musculoskeletal robots, appear more in the bending direction. First, this study describes this design method, then describes a developed pneumatically driven tensegrity robot arm with 20 actuators. Next, the range of motion and stiffness under various driving patterns are presented as evaluations of the robot performance.