Wearable electronics are recognized as a vital tool for gathering in situ kinematic information of human body movements. In this paper, we describe the production of a core–sheath fiber strain sensor from readily available materials in a one-step dip-coating process, and demonstrate the development of a smart sleeveless shirt for measuring the kinematic angles of the trunk relative to the pelvis in complicated three-dimensional movements. The sensor’s piezoresistive properties and characteristics were studied with respect to the type of core material used. Sensor performance was optimized by straining above the intended working region to increase the consistency and accuracy of the piezoresistive sensor. The accuracy of the sensor when tracking random movements was tested using a rigorous 4-h random wave pattern to mimic what would be required for satisfactory use in prototype devices. By processing the raw signal with a machine learning algorithm, we were able to track a strain of random wave patterns to a normalized root mean square error of 1.6%, highlighting the consistency and reproducible behavior of the relatively simple sensor. Then, we evaluated the performance of these sensors in a prototype motion capture shirt, in a study with 12 participants performing a set of eight different types of uniaxial and multiaxial movements. A machine learning random forest regressor model estimated the trunk flexion, lateral bending, and rotation angles with errors of 4.26°, 3.53°, and 3.44° respectively. These results demonstrate the feasibility of using smart textiles for capturing complicated movements and a solution for the real-time monitoring of daily activities.