We calculate the forces acting upon species adsorbed on a single wall carbon nanotube, in the presence of electric currents. We present a self consistent real space Green function method, which enables us to calculate the current induced forces from an ab-initio Hamiltonian. The method is applied to calculate the force on an adsorbed O atom on a (5,5) carbon nanotube, for different bias voltages and adsorption sites. For good contact regimes and biases of the order of Volts, the presence of a current can affect the potential energy surfaces considerably. Implications of these effects for the induced diffusion of the species are analyzed. The dependence of the force with the nanotube radius is studied. In addition, the magnitude of inelastic electron scattering, inducing vibrational heating, and its influence on the adsorbates' drift, is commented.