Soft robots can create complicated structures and functions for rehabilitation. The posture perception of soft actuators is critical for performing closed-loop control for a precise location. It is essential to have a sensor with both soft and flexible characteristics that does not affect the movement of a soft actuator. This paper presents a novel end-to-end posture perception method that employs flexible sensors with kirigami-inspired structures and long short-term memory (LSTM) neural networks. The sensors were developed with conductive sponge materials. With one-step calibration from the sensor output, the posture of the soft actuator could be calculated by the LSTM network. The method was validated by attaching the developed sensors to a soft fiber-reinforced bending actuator. The results showed the accuracy of posture prediction of sponge sensors with three kirigami-inspired structures ranged from 0.91 to 0.97 in terms of R2. The sponge sensors only generated a resistive torque value of 0.96 mNm at the maximum bending position when attached to a soft actuator, which would minimize the effect on actuator movement. The kirigami-inspired flexible sponge sensor could in future enhance soft robotic development.