We have adapted the Coupled Large-scale Ice-Ocean (CLIO) model in order to include atmospheric pressure forcing in addition to the classical atmospheric forcing (heat and freshwater fluxes and wind stress). We have compared the modeled bottom pressure to in situ bottom pressure measurements and also to another ocean model. We have computed the induced effects on Earth orientation parameters (polar motion and nutations) and also on Earth time-variable gravity field. We show that the response of the ocean to atmospheric pressure forcing has geodetic consequences well above the precision level and that the response of CLIO seems reasonable with respect to the few data sets we can compare with. We also show that the results obtained from the model improve the modeling of polar motion.