In view of existing problems, such as the seed and fertilizer supply link for wheat seeders still relying on manual installation and the lack of practical application equipment, a seed–fertilizer replenishment device based on the three-degree-of-freedom mechanical arm and screw conveying principle is designed using the seed box installation and supply as the operation scenario to replace the manual installation process. Combined with the requirements of the seed box replenishment operation, the key parameters of the replenishment robot arm and the screw conveyor auger are determined. Then, the kinematic model of the replenishment robot arm is established based on the modified D-H method, forward and inverse kinematics calculations are performed, and the workspace is analyzed using the Monte Carlo method. Based on this, the robotic arm task path is designed, the fifth-degree polynomial interpolation method is used to complete the trajectory planning, and MATLAB R2016a software is used to simulate the motion trajectories of each joint, verifying the feasibility of the trajectory planning solution. Finally, a prototype is trial-produced and quadratic regression orthogonal testing and response surface analyses are conducted to obtain the optimal working parameters of the replenishment device. The verification test shows that when the angular velocity of the lumbar joint of the replenishment device is 4°/s, the speed of screw conveyor is 90 r/min, and the angle of the big arm is 12°, the conveying loss rate is 3.98%, and the conveying efficiency is 0.833 kg/s. The relative errors with the theoretical optimal values are 4.2% and 2.4%, respectively, both less than 5%. The supply trajectory is reasonable, and the robot arm runs smoothly. This study can provide reference for the design of seed–fertilizer replenishment device for wheat seeders.