In this study, a soft robotic finger with variable stiffness and tunable bending shape capability is proposed. The finger employs shape memory polymers (SMP) as the variable stiffness element and polyimide (PI) electrothermal films as the flexible heaters for segmental heating. SMP and PI electrothermal films constitute the variable stiffness structure. The SMP part exhibits a reversible transition from glass state to rubber state during the heating/cooling process. The whole transition process results in an elastic modulus range of three orders of magnitude. The finger can obtain multiple bending shapes and adapt to the outer contours of diverse objects because of the segmental stiffness modulation capability of the variable stiffness structure. Supercoiled polymer artificial muscles (SCPAMs) are used as actuators for the finger. SMPs and SCPAMs are thermoresponsive and can be activated by thermal heating with electricity, making the whole finger structure compact. Experimental results show that the stiffness of the finger at room temperature (25 °C) is 10.54 times that at 70 °C when the actuators are on. The performance of the finger is further validated via the sequential motion demonstration and grasping tests with variable stiffness and bending shape control capabilities, showing the proposed design’s potential in soft grippers and robotic design.