Using a simple quantum-mechanical model, we explore a tunneling anisotropic magnetoresistance (TAMR) effect in ferroelectric tunnel junctions (FTJs) with a ferromagnetic electrode and a ferroelectric barrier layer, which spontaneous polarization gives rise to the Rashba and Dresselhaus spin-orbit coupling (SOC). For realistic parameters of the model, we predict sizable TAMR measurable experimentally. For asymmetric FTJs, which electrodes have different work functions, the built-in electric field affects the SOC parameters and leads to TAMR dependent on ferroelectric polarization direction. The SOC change with polarization switching affects tunneling conductance, revealing a new mechanism of tunneling electroresistance (TER). These results demonstrate new functionalities of FTJs which can be explored experimentally and used in electronic devices.