A novel method to design leaky-wave antennas radiating vortex cylindrical Airy beams at microwave frequencies is here presented. Two different approaches are adopted to produce waves with a nonzero orbital angular momentum (OAM): one based on a bull's eye design excited by a uniform circular array of vertical coaxial probes with proper azimuthal phase delay, and one based on a single coaxial feeder exciting a multi-spiral radiator. Both of them take advantage of backward radial propagation of cylindrical leaky waves promoting circular Airy beams with vortex patterns. The OAM state can be changed by either varying the probe phasing or the number of spiral units. A reference profile is designed under transverse-electric and transverse-magnetic excitation independently. Numerical full-wave analysis are performed using different angular states to validate the antenna design, as well to highlight the different …