Orbital angular momentum (OAM) is a new dimension for improving channel capacity and has been widely studied by scientists. In recent years, there has been an increasing amount of research on antennas and electromagnetic (EM) beams containing OAM, demonstrating its excellent ability in communication. This article proposes a Ka-band multi-mode orbital angular momentum reflectarray antenna (RA) capable of generating four vortex EM beams with four modes (l = −1, 0, +1, +2). The proposed unit cell can cover a 360-degree reflection phase range with a magnitude above 0.88, achieved through a combination of variable-sized and delay-line units. Furthermore, the unit cell’s mirror configuration allows for cross-polarization rejection. Based on these unit cells, a square reflectarray antenna (25 × 25 elements) is designed, fabricated, and measured. The measured results demonstrate that the 1 dB bandwidths for four modes are 25.81% (27–35 GHz, l = −1), 31.25% (27–37 GHz, l = 0), 28.57% (27–36 GHz, l = +1), and 20.69% (26–32 GHz, l = +2), respectively. Notably, the 3 dB gain bandwidths of all modes exceed 40%, with the maximum 3 dB bandwidth reaching 47.62% at mode l = +1. Furthermore, all vortex EM beams of this proposed RA maintain mode purities exceeding 70% within 3 dB bandwidths.