In thermodynamics, there exists a conventional belief that ''the Carnot efficiency is reachable only when a process is reversible.'' However, there is no theorem proving that the Carnot efficiency is unattainable in an irreversible process. Here, we show that the Carnot efficiency is reachable in an irreversible process through investigation of the Feynman-Smoluchowski ratchet (FSR). We also show that it is possible to enhance the efficiency by increasing the irreversibility. Our result opens a new possibility of designing an efficient heat engine in a highly irreversible process and also answers the long-standing question of whether the FSR can operate with the Carnot efficiency.