In this paper, a new sparse transmitting and receiving array is designed to improve the joint angle and polarization parameter estimation performance for bistatic electromagnetic vector sensors Multiple-Input Multiple-Output radar. Firstly, large array aperture can be obtained with the aid of the sparse transmitting and receiving array. Then, an effective third-order tensor model is constructed in order to make full use of the multidimensional space-time characteristics of output data after matching filtering. And, the Parallel Factor trilinear alternating least square algorithm is proposed to deal with the constructed third-order tensor model, which can yield closed-form automatically paired two dimensional Direction of Departure and two dimensional Direction of Departure estimation without additional angle pair matching process. Furthermore, two sets of high accuracy rotation invariance relationships corresponding to transmit elevation angle and receive elevation angle can be achieved by using the estimated transmit steering vector matrix and receive steering vector matrix. After the accuracy transmit elevation angle and receive angle are obtained, the corresponding transmitting and receiving azimuth angle, polarization angle and polarization phase difference can be accurately estimated by using the vector-cross-product algorithm. Compared with existing algorithms, the proposed algorithm can avoid high dimensional eigenvalue decomposition and additional parameter matching process. Moreover, the high estimation performance of the proposed can be further guaranteed by using the designed sparse array. Finally, simulation results demonstrate the effectiveness and superiority of the proposed method in terms of estimation accuracy and angle resolution.