Free space optical communication (FSO) is widely deployed to transmit high data rates for rapid communication traffic increase. Asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) modulation is a very efficient FSO communication technique in terms of transmitted optical power. However, its performance is limited by atmospheric turbulence. When the channel includes strong turbulence or is non-deterministic, the bit error rate (BER) increases. To reach optimal performance, the ACO-OFDM decoder needs to know accurate channel state information (CSI). We propose novel detection using different deep learning (DL) algorithms. Our DL models are compared with minimum mean square error (MMSE) detection methods in different turbulent channels and improve performance especially for non-stationary and non-deterministic channels. Our models yield performance very close to that of the MMSE estimator when the channel is characterized by weak or strong turbulence and is stationary. However, when the channel is non-stationary and variable, our DL model succeeds in improving the performance of the system and decreasing the signal to noise ratio (SNR) by more than 8 dB compared to that of the MMSE estimator, and it succeeds in recovering the received data without needing to know accurate CSI. Our DL decoders also show notable speed and energy efficiency improvement.