Thermal convection under the influence of rotation appears in a wide range of engineering and geophysical applications, and has been investigated extensively both experimentally and numerically utilizing different canonical configurations. The problem of radial convection in a cylindrical annulus, studied in the present work, has received less attention than other configurations, such as rotating Rayleigh-Bénard convection. It has long been known that rotation has a stabilizing effect and, in the limit of strong rotation, a two-dimensional flow emerges, resulting in reduced heat transfer rates. Here, direct numerical simulations are performed for buoyancy-driven flows in a cylindrical annulus bounded by two parallel disks with and without rotation. By maintaining a radial gravity term analogous to a centrifugal acceleration even in the stationary cases, it is possible to isolate the effect of the Coriolis force on the flow. As expected, when rotation is imposed the flow is characterized by large-scale structures and the heat transfer rates are significantly reduced. Turbulence statistics are presented for the mean temperature profiles, temperature and velocity fluctuations, turbulent kinetic energy budgets, and Reynolds stress anisotropy tensor. It is shown that rotation significantly affects the distribution of turbulent kinetic energy throughout the radial direction, in particular away from the cylindrical surfaces. The anisotropy maps reveal that the turbulence is quasi-two-dimensional in the rotating cases, even for the highest value of Ra considered, whereas without rotation the core region approaches the isotropic limit with increasing Ra.