A wideband millimeter-wave (mmWave) circularly polarized (CP) complementary antenna array is proposed herein for radio-frequency energy harvesting (RFEH) applications. The element is constructed of a CP magneto-electric (ME)-dipole antenna and innovatively introduces the complementary source technique to improve the CP radiation performance. The detailed analyses are provided to elaborate the operating principles of the element. Simulated results for the element reveal an impedance bandwidth of 25.7%, a 3-dB axial ratio (AR) bandwidth of 24.8%, and a gain of 8.7 ± 1.6 dBic over the spectrum. The element shows the stable radiation pattern and wide AR/impedance overlapping bandwidth (33.87–43.15 GHz) for RFEH applications covering the 35-, 37-, and 39-GHz bands. To enhance the gain for practical applications, the element is employed in the design, fabrication, and testing of a planar <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times $ </tex-math></inline-formula> 4 array fed by a full-corporate substrate-integrated waveguide (SIW) network. Measured results indicate that the array achieves an impedance bandwidth of 20.2%, a 3-dB AR bandwidth of 24.3%, and a 3-dB gain bandwidth of 22.8%. Thus, the proposed array features a low profile and excellent performance, which makes it a desirable candidate for mmWave RFEH applications.