Diffusion weighted magnetic resonance imaging (DW-MRI) of fetal brain is challenged by fetal and maternal motion, low signal-to-noise ratio and short scan times. Hence, there is a need for methods that can accurately estimate the parameters of interest from small numbers of noisy measurements. We propose a deep learning method for accurate and robust estimation of color fractional anisotropy as a measure of brain architecture from fetal DW-MRI scans. We also propose methods for simulating realistic training data. Evaluations on an independent cohort of fetal DW-MRI scans show that the proposed method is significantly more accurate than standard methods.