This work presents a design of an aperture-coupled complementary antenna for realizing circularly polarized (CP) broadside radiation at millimeter-wave (mm-wave) frequencies. The proposed antenna constructively combines a patch dipole (electric dipole radiation) and a folded loop antenna (magnetic dipole radiation), which are differentially excited by a longitudinal slot etched on the top layer of the substrate integrated waveguide (SIW). The combination of the proposed patch dipole and the folded loop antenna results in a paralleled electric dipole and magnetic dipole which can generate two orthogonal electric field components and 90° phase difference in the far-field radiation when they are in-phase excited. The proposed antenna achieves a wide impedance bandwidth of 46% from 48.47 to 77.46 GHz and a wide 3 dB axial ratio bandwidth (ARBW) of 47.3% from 51.64 to 83.61 GHz with an overlapped bandwidth of 40%. To further enhance the antenna gain, sequential rotation technique is adopted to construct a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> subarray, which is further employed in a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> subarray. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> subarray is then used to construct an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8 \times 8$ </tex-math></inline-formula> antenna array, which achieves a wide impedance bandwidth of 33.8% from 56.11 to 78.95 GHz and a wide 3 dB ARBW of 38.8% from 53.57 to 79.32 GHz, with a maximum antenna gain of around 25.2 dBic. The proposed antenna element and array design would be a competitive candidate for future wireless applications operating at mm-wave spectrum.