Electro-adhesive clutches have become effective tools for variable stiffness functions in many robotic systems due to their light weight, high speed and strong brake force. In this paper, we present a novel, tubular design of an electro-adhesive clutch. Our clutch consists of flexible electrode sheets rolled into a tubular structure. This design allows encapsulating large electrode areas in a compact size for strong brake force. Additionally, the tubular structure acts as a guide for directional sliding without external guides. The structure also ensures that the electrode surfaces are encapsulated, preventing the accumulation of dust and thus leading to reliable performance. This structure is therefore an improvement over the commonly used planar designs. The characterization of the electro-adhesive tubular clutch shows that the frictional force increases with the increase of the electrode contact area, the decrease of the roll diameter and the dielectric layer thickness. A retractable tubular clutch is made by fixing an elastic cable along the clutch axis and achieves a stiffness change factor up to 260. Applications of this retractable clutch in robotics to achieve variable stiffness are demonstrated in two systems: a tensegrity structure and a wing skeleton. Changes in stiffness by 13.2 and 30.2 times are achieved for the two systems, respectively. The proposed tubular clutch is an effective means of achieving variable stiffness, particularly in the case of robotic systems that transmit forces through tensioned cables.