Accurate torque sensing is essential for robotic actuators using harmonic drives, yet physical torque sensors add cost, complexity, and mechanical vulnerability. This paper presents a deep-learning-based method for estimating actuator output torque without dedicated sensors. We propose an LSTM neural network trained on data from motor current and three encoder signals, which capture the dynamic behavior of a custom-built actuator with a compliant tube. By learning from time-series data, the LSTM model accounts for nonlinearities such as friction and hysteresis. Experimental results show that the proposed model predicts output torque with high accuracy, achieving a root mean squared error of just 0.6578 Nm—under 4% of the applied torque range. The model successfully tracks dynamic torque variations and captures hysteresis behavior, demonstrating its effectiveness as a sensorless estimation strategy. This approach offers a cost-effective and robust solution for torque-controlled robotic systems, particularly in applications like collaborative robots and exoskeletons.