We introduce and theoretically describe internally twisted optical metamaterials, in which the metamolecules can have an arbitrary, but common, orientation in the unit cells. The molecules, and consequently the material, are not chiral, but they are allowed to be noncentrosymmetric. While such internally twisted crystalline structures are difficult to find in natural materials, metamaterials of this type can be designed and fabricated at will. Here, we present a theoretical method that enables a detailed analysis of such metamaterials. The method establishes a connection between the optical properties of a metamaterial and the plane-wave optical response of a single two-dimensional array of metamolecules. In the theory, the effective wave parameters, such as the refractive index and wave impedance, are retrieved. Using the model, we show that these parameters can dramatically depend on the wave propagation direction and metamolecular orientation, which can be used, along with optical anisotropy, to efficiently adjust and control the plane-wave content of optical beams.