Internet of Things (IoT) is a new emerging paradigm which requires billions of wirelessly connected devices that communicate with each other in a complex radio-frequency (RF) environment. Considering the huge number of devices, recharging batteries or replacing them becomes impractical in real life. Therefore, harvesting ambient RF energy for powering IoT devices can be a practical solution to achieve self-charging operation. The antenna for the RF energy harvesting application must work on multiple frequency bands (multiband or wideband) to capture as much power as possible from ambient; it should be compact and small in size so that it can be integrated with IoT devices; and it should be low cost, considering the huge number of devices. This thesis presents a fully printed 3D cube Cantor fractal RF energy harvesting unit, which meets the above-mentioned criteria. The multiband Cantor fractal antenna has been designed and implemented on a package of rectifying circuits using additive manufacturing (combination of 3D inkjet printing of plastic substrate and 2D metallic screen printing of silver paste) for the first time for RF energy harvesting application. The antenna, which is in a Cantor fractal shape, is folded on five faces of a 3D cube where the bottom face accommodates rectifying circuit with matching network. The rectenna (rectifying antenna) harvests RF power from GSM900, GSM1800, and 3G at 2100 MHz frequency. Indoor and outdoor field tests of the RF energy harvester have been conducted in the IMPACT lab and the King Abdullah University of Science and Technology (KAUST) campus territory, and 252.4 mV of maximum output voltage is harvested.