Gait asymmetry, a consequence of various neurological or physical conditions such as aging and stroke, detrimentally impacts bipedal locomotion, causing biomechanical alterations, increasing the risk of falls and reducing quality of life. Addressing this critical issue, this paper introduces a novel diagnostic method for gait symmetry analysis through the use of an assistive robotic Smart Walker equipped with an innovative asymmetry detection scheme. This method analyzes sensor measurements capturing the interaction torque between user and walker. By applying a seasonal-trend decomposition tool, we isolate gait-specific patterns within these data, allowing for the estimation of stride durations and calculation of a symmetry index. Through experiments involving 5 experimenters, we demonstrate the Smart Walker's capability in detecting and quantifying gait asymmetry by achieving an accuracy of 84.9% in identifying asymmetric cases in a controlled testing environment. Further analysis explores the classification of these asymmetries based on their underlying causes, providing valuable insights for gait assessment. The results underscore the potential of the device as a precise, ready-to-use monitoring tool for personalized rehabilitation, facilitating targeted interventions for enhanced patient outcomes.