Wankel pump designs have not been fully established, with existing designs limited to bicornous rotor pumps and triangular rotor pumps. Here, on the basis of Wankel geometry, we present a tetragonal rotor pump with a three-lobe epicycloid and its conjugate envelope as chamber and rotor profile. First, the design method and basic working principle of the pump are introduced. Four groups of prototypes with different shape factors were manufactured, and their flow and pressure characteristics were experimentally studied. Numerical study showed that the flow rate irregularity of the pump is lower than that of existing Wankel pumps. Finally, the feasibility the pump for mixing applications was verified by a flow field observation experiment. The work in this paper provides a new type of rotary displacement pump design, representing an study of reverse application of a Wankel engine structure.