This work presents an application of self-attention networks for cryptocurrency trading. Cryptocurrencies are extremely volatile and unpredictable. Thus, cryptocurrency trading is challenging and involves higher risks than trading traditional financial assets such as stocks. To overcome the aforementioned problems, we propose a deep reinforcement learning (DRL) approach for cryptocurrency trading. The proposed trading system contains a self-attention network trained using an actor-critic DRL algorithm. Cryptocurrency markets contain hundreds of assets, allowing greater investment diversification, which can be accomplished if all the assets are analyzed against one another. Self-attention networks are suitable for dealing with the problem because the attention mechanism can process long sequences of data and focus on the most relevant parts of the inputs. Transaction fees are also considered in formulating the studied problem. Systems that perform trades in high frequencies cannot overlook this issue, since, after many trades, small fees can add up to significant expenses. To validate the proposed approach, a DRL environment is built using data from an important cryptocurrency market. We test our method against a state-of-the-art baseline in two different experiments. The experimental results show the proposed approach can obtain higher daily profits and has several advantages over existing methods.