We propose an alternative conceptual design for a graphene-based quantum engine, driven by a superposition of mechanical strain and an external magnetic field. Engineering of strain in a nanoscale graphene flake creates a gauge field with an associated uniform pseudomagnetic field. The strain-induced pseudomagnetic field can be combined with a real magnetic field, leading to the emergence of discrete relativistic Landau levels within the single-particle picture. The interlevel distance and hence their statistical population can be modulated by quasistatically tuning the magnetic field along a sequence of reversible transformations that constitute a quantum mechanical analog of the classical Otto cycle.