In this work, I developed a two-dimensional active acoustic metamaterial with controllable anisotropic density. The material consists of composite lead–lead zirconate titanate plates clamped to an aluminum structure with air as the background fluid. The effective anisotropic density of the material is controlled, independently for two orthogonal directions, by means of an external static electric voltage signal. The material is used in the construction of a reconfigurable waveguide capable of controlling the direction of the acoustic waves propagating through it. An analytic model based on the acoustic two-port theory, the theory of piezoelectricity, the laminated pre-stressed plate theory, and the S-parameters retrieval method was developed to predict the behavior of the material. The results were verified using a finite element model developed using ANSYS APDL. Excellent agreement is found between both models for the studied frequency and voltage ranges. The results show that, below 1600 Hz, the density is controllable within orders of magnitude relative to the uncontrolled case. The results also suggest that simple controllers could be used to program the material density toward full control of the directivity and dispersion characteristics of acoustic waves.