Various machine translation (MT) studies were conducted for resource-rich languages such as English, Chinese, and others. However, research on MT from English to Ethiopian languages and vice versa was still in its infancy due to the low resource limitations of the Ethiopian languages. Anuak is one of the languages spoken in Ethiopia and South Sudan, which is very low-resourced and severely lacking in computational linguistic tools. To overcome this problem, this research investigates the development of bidirectional English-Anuak via a deep learning approach. A total of 26,448 sentences of a bilingual parallel text corpus were collected, and various preprocessing tasks were applied to the corpus to make it ready for the development of models. The corpus was divided into 80% (21,158 sentences) for training and 20% (5,290 sentences) for testing the models. Deep learning models, namely long short-term memory (LSTM), bidirectional LSTM (BiLSTM), gated recurrent unit (GRU), and bidirectional GRU (BiGRU) without attention and with attention mechanisms, as well as transformer models, were developed for bidirectional English-Anuak MT. Several experiments were conducted to find the optimal values of the hyperparameters of the models. Using the optimal hyper parameters, all the models were trained and evaluated using the BLEU score evaluation metrics. The results show that a transformer model was the best performing model, with BLEU scores of 32.31 and 33.65 for English-Anuak and Anuak-English, respectively. Overall, the recurrent neural network variants and transformer models are suitable for developing the bidirectional MT for English-Anuak languages.