A convolutional neural network (CNN) for broadband direction of arrival (DOA) estimation of far-field electromagnetic signals is presented. The proposed algorithm performs a nonlinear inverse mapping from received signal to angle of arrival. The signal model used for algorithm is based on the circular antenna array geometry, and the phase component extracted from the spatial covariance matrix is used as the input of the CNN network. A CNN model including three convolutional layers is then established to approximate the nonlinear mapping. The performance of the CNN model is evaluated in a noisy environment for various values of signal-to-noise ratio (SNR). The results demonstrate that the proposed CNN model with the phase component of the spatial covariance matrix as the input is able to achieve fast and accurate broadband DOA estimation and attains perfect performance at lower SNR values.