This paper presents the SMARoll robot which is a modular closed-chain rolling robot with compliant shape memory alloy (SMA) actuators that can mimic the behavior of rolling animals. The SMARoll robot can provide advanced mobility, controllability, terrain adaptability and modularity/scalability. It also has the capability to overcome obstacles and snags that might be useful to explore unstructured/rugged environments. The robot consists of twelve links and joints. It is actuated by a novel SMA rotating actuator at each joint which provides compliance/flexibility advantage to the robot. The rotating actuator is fabricated in a novel manner by sewing a SMA wire between two rotating frames. Kinematic analysis for the SMARoll robot is studied to determine the configuration of the entire robot considering links’ position and orientation as a function of joint angles. At an equilibrium position, the SMARoll robot is mostly resting on four links. To move the robot's center of mass and the whole robot, the locomotion of the robot can be divided into steps. At each step, only four (2 active and 2 passive) joint motions are required for this robot locomotion strategy. Experimental work is performed to validate the robot design and kinematic analysis and prove locomotion strategy. The experimental results show that the robot has a good capability to achieve terrain adaptability due to compliance advantage. Also, results show that the robot is capable to achieve a speed of 0.13 m/s at plain ground.