Molecular communication (MC) is getting closer to becoming a next-generation communication technology with many applications in life sciences and other industrial applications. Multiple techniques have been proposed on how to design MC receivers depending on the channel characteristics. Experimentally, first testbeds also demonstrate the potentialities for communication using molecules as carriers. In this paper, we focus on developing a reinforcement learning (RL)-based receiver, targeting a realistic scenario with testbed measurements, and addressing transmitter mobility. Leveraging on reported solutions for machine learning (ML) methods, we demonstrate the usability of an RL agent to synchronize the receiver to the received signal. We evidence the learning capabilities of the agent to compensate for the impact of mobility, achieving a low probability of missed detection and small misalignment with the symbol time.