Adaptive optics (AO) systems are used in ground- based telescopes to improve image resolutions, especially for long-exposure photography, by compensating for the effects of atmospheric turbulence and internal vibrations. Most current AO systems are based on simple control laws that either neglect the temporal correlation in atmospheric turbulence, use a simplified system model, or both. This paper presents a direct data-driven control scheme to compute an optimal controller using the frequency-domain representation of the disturbance and the system model. Numerical simulations of the AO system demonstrate performance improvement compared to standard AO control schemes, and resilience to the variance in atmospheric turbulence and internal vibrations.