Wireless power transfer (WPT) using magnetic-coupling resonant has been proved to be a promising transmission method. At present, most of the existing resonant WPT systems adopt integer-order inductors and capacitors. In fact, in addition to integer-order components, there also exists fractional-order inductors and capacitors, which possess richer characteristics than integral-order inductors and capacitors. However, there are few studies on the application of fractional-order components in resonant WPT system. Therefore, this paper proposes a fractional-order resonant WPT system, which is based on a fractional-order resonant circuit only incorporating a fractional-order capacitor. The coupled-mode theory model of the proposed WPT system is established, and the impact of different loads and orders on transfer characteristics is explored. The theoretical analysis demonstrates that the proposed system can achieve constant current output that is independent of load, just by choosing appropriate parameters of the fractional-order capacitor. Finally, an experimental prototype of the fractional-order resonant WPT system is built, and the experiment results verify the correctness of the theoretical analysis.