Integrating social robots into daily life has elevated the demands for robot anthropomorphism to enhance Human-Robot Interaction (HRI). Through the intelligent design process, this study adapted the robot's social presence model to examine the mediating effect of robot social presence on the relationships between robot anthropomorphism and users' perceived affinity. The study adopted a 2 (appearance anthropomorphism: low vs. high) × 2 (interaction anthropomorphism: low vs. high) mixed factorial research method, with appearance anthropomorphism as the between-subjects factors, interface anthropomorphism as the within-subjects factor, social presence variables as the mediators, and users' perceived affinity as the dependent variable. Student participants (N = 218) were recruited for an online survey concerning this research topic. The results indicated the positive main effect of robot interaction anthropomorphism and interaction effect on users' perceived affinity, but not appearance anthropomorphism. The mediating role of perceived social presence was supported, and the uncanny valley effect was confirmed on interaction anthropomorphism. Robot stimuli were successfully manipulated via intelligent design processes. Robot interaction anthropomorphism positively influences users' perceived affinity, and the robot's social presence plays a crucial mediating role in the relationship. Significant interaction effect highlighted the potential application of domestic social robots with high appearance and high interaction anthropomorphism in future family scenarios.