Robotic bin packing is very challenging, especially when considering practical needs such as object variety and packing compactness. This paper presents SDF-Pack, a new approach based on signed distance field (SDF) to model the geometric condition of objects in a container and compute the object placement locations and packing orders for achieving a more compact bin packing. Our method adopts a truncated SDF representation to localize the computation, and based on it, we formulate the SDF minimization heuristic to find optimized placements to compactly pack objects with the existing ones. To further improve space utilization, if the packing sequence is controllable, our method can suggest which object to be packed next. Experimental results on a large variety of everyday objects show that our method can consistently achieve higher packing compactness over 1,000 packing cases, enabling us to pack more objects into the container, compared with the existing heuristics under various packing settings.