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The Global Positioning System (GPS) has been widely applied in outdoor positioning, but it cannot meet the accuracy requirements of indoor positioning. Comprising an important part of the Internet of Things perception layer, Radio Frequency Identification (RFID) plays an important role in indoor positioning. We propose a novel localization scheme aiming at the defects of existing RFID localization technology in localization accuracy and deployment cost, called ANTspin: Efficient Absolute Localization Method of RFID Tags via Spinning Antenna, which introduces a rotary table in the experiment. The reader antenna is fixed on the rotary table to continuously collect dynamic data. When compared with static acquisition, there is more information for localization. After that, the relative incident angle and distance between tags and the antenna can be analyzed for localization with characteristics of Received Signal Strength Indication (RSSI) data. We implement ANTspin using COTS RFID devices and the experimental results show that it achieves a mean accuracy of 9.34 cm in 2D and mean accuracy of 13.01 cm in three-dimensions (3D) with high efficiency and low deployment cost.