An elegant combination of electric near-field phase transformation technique and electromagnetic-wave refraction, implemented through a pair of 3D printed dielectric structures, has been used to demonstrate a Ka-band beam-scanning antenna system. The system comprises a resonant-cavity antenna (RCA), which is used as a base antenna, a stepped dielectric (SD), and a dielectric wedge (DW). The SD is suspended above RCA in the near-field region to focus its broadside beam at an offset angle of 20°. The DW is placed above the SD and its two opening angles are selected such that the offset-angle focused beam tilts further and moves back to the broadside when the DW is co- and counter-aligned with the SD, respectively. The total height of the antenna system is 8:1λ0, where λ0 is the free-space wavelength at the operating frequency of 30 GHz. The total cost of the material used for printing the two dielectric structures in prototyping is only 6 USD. It has been demonstrated through measurements of the prototype that by rotating the DWaround its own axis, the antenna beam can be scanned in both azimuth and elevation planes. The measured results indicate that antenna beam can effectively be scanned to any arbitrary angular position within a conical region having an apex angle of 68°, while maintaining peak-gain value within the 3 dB limit of the maximum gain of 16 dBi.