Context. Thermal tides can torque the atmosphere of hot Jupiters into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star.Aims. In this work, our goal is to characterize the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal forcing of its host star by identifying the structure of tidal waves responsible for variation of mass distribution, their dependence on the tidal frequency, and their ability to generate strong zonal flows.Methods. We develop an ab initio global modelling that generalizes the early approach of Arras & Socrates (2010, ApJ, 714, 1) to rotating and non-adiabatic planets. We analytically derive the torque exerted on the body and the associated timescales of evolution, as well as the equilibrium tidal response of the atmosphere in the zero-frequency limit. Finally, we numerically integrate the equations of thermal tides for three cases, including dissipation and rotation step by step.Results. The resonances associated with tidally generated gravito-inertial waves significantly amplify the resulting tidal torque in the range 1–30 days. This torque can globally drive the atmosphere into asynchronous rotation, as its sign depends on the tidal frequency. The resonant behaviour of the tidal response is enhanced by rotation, which couples the forcing to several Hough modes in the general case, while the radiative cooling tends to regularize it and diminish its amplitude.