The robot arm is a multi-input, multi-output and non-linear system that has many industrial applications. The parameter uncertainties and external disturbances attenuate the performance of this system and controller design is necessary to overcome them. In this paper, the interval Type II fuzzy fractional-order proportional integral differential (IT2FO-FPID) controller is designed to control the robot arm with 2 degrees of freedom (two-link robot arm). Whale Optimization Algorithm (WOA) is used to determine the optimal value of controller parameters. The performance of IT2FO-FPID is compared with PID, fractional-order PID (FOPID) and Fuzzy FOPID whose parameters are determined by WOA. The performance of IT2FO-FPID whose parameters are determined by WOA, genetic algorithm, and particle swarm optimization are compared. Quantitative and qualitative results of simulations indicate performance improvement with the IT2FO-FPID controller. The ability of WOA in optimizing the parameters of the IT2FO-FPID controller is demonstrated. Sensitivity analysis and the study of the effect of parameter variations and disturbances confirm the robust performance of WOA-based IT2FO-FPID.