The positron states in the perfect GaAs lattice and at fully relaxed vacancies with different total charges have been calculated. Moreover, the metastable configuration of the As anti-site in GaAs proposed as a model for the EL2 defect is considered. The atomic structures of the defects are taken from recent ab initio molecular dynamics calculations. The positron states and the ensuing positron annihilation rates and trap binding energies have been determined by the method based on the superposition of atomic electron densities. A comparison of the results with experimental data shows that, while the present theoretical approach gives a consistent and qualitative interpretation, it fails to reproduce the trapped state lifetimes quantitatively. It is shown that a localized positron can affect the lattice relaxations around the defect. Therefore, it is suggested that the positron should be treated fully self-consistently, simultaneously with electrons, in the ab initio molecular dynamics in order to determine the way in which the localized positron affects the electron structure and ionic relaxation near the vacancy.