This study presents the design of a lower limb-worn, soft wearable robot that assists ankle plantar flexion using soft textiles and a shape memory alloy (SMA) wire actuator. Textile-based clothing-type soft wearable robots, the smart clothes in short, are proposed to build a soft exoskeleton that is inherently lightweight and comfortable for the wearer. SMA wire actuators are embedded in the smart clothes to provide assistive forces to the wearer. The SMA wire actuator is a low-profile wire-type artificial muscle actuator, which can be embedded on the textile without any extruded parts on the clothing. We have built an SMA wire actuator-embedded smart clothing that is able to provide ankle assistive force without rigid kinematic mechanisms. The smart clothing has a mass of 428.5 g without a power battery, and it can generate an ankle moment of 100 N cm in each ankle during walking.