Rotating gantries are commonly used in ion-therapy facilities to assist and support optimizing the dose distribution delivered to the patient. They are installed at the end of the beamlines and rotated mechanically in the treatment room. In synchrotron-based facilities, the gantries must be able to transport slowly extracted beams with essentially different emittance patterns in the two transverse planes. Such beams will be referred to as the asymmetric beams. A special device called rotator has been proposed as a possible solution. The worldwide first beamline with the rotator has been recently commissioned. The original rotator concept uses an “external” rotator that is a part (a module) of the beamline the gantry is connected to. In this paper, a novel gantry ion-optical concept integrating the rotator optics into the gantry optics is introduced. The first-order gantry transfer matrix satisfies the so-called sigma-matching ion-optical constraints, and—at the same time—it possesses the format of a rotator transfer matrix. The rotator-matching and the sigma-matching principles are combined in the gantry transfer matrix, which means that the sigma-matching gantry acts simultaneously as a rotator without the need for an extra rotator device. In addition, scattering in the gantry nozzle is used to balance the asymmetric beam emittances in the two transverse planes without an additional scattering foil. In this way, the presented ion-optical concept combines all three known matching techniques—the sigma matching, the rotator matching, and the scattering-foil matching—within the gantry beam transport system. Such a beam transport system provides the best matching result and full angular independence of the beam parameters at the gantry isocenter. It also makes it possible to optimize the beam parameters not only at the gantry isocenter but also at the beam monitors located in the gantry nozzle without increasing the number of gantry quadrupoles. There are two possible versions of such gantry optics: the point-to-point and the parallel-to-point optics. They both are presented in this paper. Theoretical calculations are supported by beam transport simulations performed with the in code. Feasibility of the newly proposed ion-optical concept is demonstrated on the MedAustron proton gantry. However, it can be applied to any rotating gantry at any ion-therapy facility. The presented design is the first rotatorlike gantry ion-optical concept worldwide. Published by the American Physical Society 2024