The Aharonov-Bohm (AB) problem for vector bosons by the Duffin- Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-1/2 AB problem. Using a boundary condition at the origin based on the self-adjoint extension method, we study the scattering and bound states problems. Expressions for S matrix, phase shift and bound states are obtained.