Trans-esophageal echocardiography (TEE) is a miniatured intra-operative ultrasound system, widely used in routine diagnosis and interventional procedure monitoring, to assess cardiac structures and functions. As a way to assist the operation of TEE remotely, we have developed an add-on robotic system to actuate a commercial TEE probe. For the proposed robot, understanding the inverse kinematics (IK) which relates the probe pose to the joint parameters is the fundamental step towards automatic control of the system. Rather than using conventional numerical-based techniques which may have problems with speed, convergence, and stability when applying to the TEE robot, this paper explores a soft computing approach by constructing an Adaptive Neuro-Fuzzy Inference System (ANFIS) to learn from training data generated by the forward kinematics (FK) and then computing the inverse kinematics in order to control the orientation of the TEE probe. With 1900 training data over 40 epochs, the minimum training error for each joint parameter was found to be less than 0.1 degree. Validation using a separate data set has indicated that the maximum error was less than 0.3 degree for each joint parameter. It is therefore concluded that the ANFIS-based approach is an effective way, with acceptable accuracy, to compute the inverse kinematics of the TEE robot.