Recently, frequency-modulated continuous wave (FMCW) radars with array antennas are gaining in popularity on a wide variety of commercial applications. A usual approach of the range and angle estimation of a target with an array FMCW radar is to form a range-angle matrix with deramped receive signal, and then apply the two-dimensional fast Fourier transformation (2D-FFT) on the range-angle matrix. However, such frequency estimation approaches give bias error because two frequencies on the range-angle matrix are not independent to each other, unlike the 2D angle estimation with a passive planar antenna array. We propose a new maximum-likelihood based algorithm for the joint range and angle estimation of multiple targets with an array FMCW radar, and show that the proposed algorithm achieves the Cramer-Rao bounds (CRBs) both for the range and angle estimation. The proposed algorithm is also compared with other algorithms for a simultaneous localization and mapping (SLAM) problem.