Radio direction finding system is a system that determines the direction or coordinates of radio signal sources. The main function of this system is to determine the direction of arrival (DOA) of an incident radio wave. DOA information plays an important role in array signal processing and has many applications in communications, radar, seismic survey, etc. In this study, we propose a method to estimate the DOA by using the simulated signal dataset obtained at the linear antenna array (ULA) and the suitable Long Short-Term Memory (LSTM) network model. The performance of the method is evaluated based on the root mean square error (RMSE) parameter and then is compared with 2 other algorithms, multiple signal classification (MUSIC) and deep neural network (DNN) in different cases such as deviation of incoming signals, variation of signal-to-noise ratio (SNR), and coherent incoming signals. The obtained results have shown that the proposed method has significantly improved accuracy compared to other methods.