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By imitating biological microswimmers, microrobots can be designed to accomplish targeted delivery of cargos and biomedical manipulations at microscale. However, it is still a great challenge to enable microrobots to maneuver in a complex environment. Machine learning algorithms offer a tool to boost mobility and flexibility of a synthetic microswimmer, hence could help us design truly smart microrobots. In this work, we investigate how a model of sea urchin sperm cell can self-learn chemotactic motion in a chemoattractant concentration field. We employ an artificial neural network to act as a decision-making agent and facilitate the sperm cell to discover efficient maneuver strategies through a deep reinforcement learning (DRL) algorithm. Our results show that chemotactic behaviours, very similar to the realistic ones, can be achieved by the DRL utilizing only limited environmental information. In most cases, the DRL algorithm discovers more efficient strategies than the human-devised one. Furthermore, the DRL can even utilize an external disturbance to facilitate the chemotactic motion if the extra flow information is also taken into account by the artificial neural network. Our results provide insights to the chemotactic process of sea urchin sperm cells and also prepare guidance for the intelligent maneuver of microrobots.