This paper presents the development of a six degrees-of-freedom manipulator with soft end-effector and an inverse kinematic compensator for aerial contact manipulation. Realizing the fact that aerial manipulators can hardly achieve precise position control, a compliant manipulator with soft end-effector is first developed to moderate end-effector positioning errors. The manipulator is designed to be rigid-soft combined. The rigid robotic arm employs the lightweight but high-strength materials. The compliance requirement is achieved by the soft end-effector so that the mechanical design for the joints are largely simplified. These two features are beneficial to lighten the arm and to ensure the accuracy. In the meantime, the pneumatic soft end-effector can further moderate the probable insufficient accuracy by endowing the manipulator with compliance for impact resistance and robustness to positioning errors. With the well-designed manipulator, an inverse kinematic compensator is then proposed to eliminate lumped disturbances from the aerial platform. The compensator can ensure the stabilization of the end-effector by using state estimation from the aerial platform, which is robust and portable as the movement of the platform can be reliably obtained. Both the accuracy and compliance have been well demonstrated after being integrated into a hexarotor platform, and a representative scenario aerial task repairing the wind turbine blade-coating was completed successfully, showing the potential to accomplish complex aerial manipulation tasks.