[en] Context: Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies of excitation and damping processes in the convection zones. Aims: We develop a formalism that provides the excitation rates of non-radial global modes excited by turbulent convection. As a first application, we estimated the impact of non-radial effects on excitation rates and amplitudes of the high-angular-degree modes that are observed on the Sun. Methods: A model of stochastic excitation by turbulent convection was developed to compute the excitation rates and then successfully applied to solar radial modes. We generalise this approach to the case of non-radial global modes. This enables us to estimate the energy supplied to high-(l) acoustic modes. Qualitative arguments, as well as numerical calculations, are used to illustrate the results. Results: We find that non-radial effects for p modes are non-negligible: - For high-n modes (i.e. typically n > 3) and for high values of l, the power supplied to the oscillations depends on the mode inertia. - For low-n modes, independent of the value of l, the excitation is dominated by the non-radial components of the Reynolds stress term. Conclusions: Our numerical investigation of high-l p modes shows that the validity of the present formalism is limited to l < 500 due to the spatial separation of scale assumption. Thus, a model for very high-l p-mode excitation rates calls for further theoretical developments; however, the formalism is valid for solar g modes, which will be investigated in a paper in preparation.