We consider the f(R,T) modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor of the matter, in order to investigate the dark-matter effects on the galaxy scale. We obtain the metric components for a spherically symmetric and static spacetime in the vicinity of general relativity solutions. However, we concentrate on a specific model of the theory where the matter is minimally coupled to the geometry, and derive the metric components in the galactic halo. Then, we fix the components by the rotational velocities of the galaxies for the model, and show that the mass corresponding to the interaction term (which appears in the Einstein modified field equation) leads to a flat rotation curve in the halo of galaxies. In addition, for the proposed model, the light-deflection angle has been derived and drawn using some observed data.
