Credit card fraud detection remains a critical challenge for financial institutions, particularly due to extreme class imbalance and the continuously evolving nature of fraudulent behavior. This study investigates two complementary approaches: anomaly detection based on multivariate normal distribution and deep reinforcement learning using a Deep Q-Network. While anomaly detection effectively identifies deviations from normal transaction patterns, its static nature limits adaptability in real-time systems. In contrast, the DQN reinforcement learning model continuously learns from every transaction, autonomously adapting to emerging fraud strategies. Experimental results demonstrate that, although initial performance metrics of the DQN are modest compared to anomaly detection, its capacity for online learning and policy refinement enables long-term improvement and operational scalability. This work highlights reinforcement learning as a highly promising paradigm for dynamic, high-volume fraud detection, capable of evolving with the environment and achieving near-optimal detection rates over time.