In this paper, we introduce a novel approach to implicitly encode precise robot morphology using forward kinematics based on a configuration space signed distance function. Our proposed Robot Neural Distance Function (RNDF) optimizes the balance between computational efficiency and accuracy for signed distance queries conditioned on the robot's configuration for each link. Compared to the baseline method, the proposed approach achieves an 81.1% reduction in distance error while utilizing only 47.6% of model parameters. Its parallelizable and differentiable nature provides direct access to joint-space derivatives, enabling a seamless connection between robot planning in Cartesian task space and configuration space. These features make RNDF an ideal surrogate model for general robot optimization and learning in 3D spatial planning tasks. Specifically, we apply RNDF to robotic arm-hand modeling and demonstrate its potential as a core platform for whole-arm, collision-free grasp planning in cluttered environments. The code and model are available at https://github.com/robotic-manipulation/RNDF.