We report a 3D ab initio investigation of the dependence of above-threshold ionization of the H⁺₂ molecule on the orientation of a linearly polarized intense femtosecond laser pulse with respect to the molecular axis. The calculations were performed in the frozen nuclei approximation for the ²Σ⁺_g(1sσ_g) ground and the ²Σ⁺_u(2pσ_u) first excited electronic states, in laser pulses of seven optical cycles (19 fs) with a wavelength of 800 nm and for different intensities. The numerical procedure combines two different techniques, a grid-based split-step method to propagate the wave packet during the pulse, and a bound and scattering states B-spline basis set calculation to extract the information from the former. We show that the orientation dependence of the above-threshold ionization spectra is very sensitive to the intensity of the field and to the final electron energy. For some intensities and final electron energies the orientation dependence of the above-threshold ionization spectrum reflects directly the charge distribution of the initial state, but in general intermediate resonances of symmetry different from that of the initial state are populated during the pulse leading to a distorted bound-state charge density, and hence a more rich orientation dependence of the above-threshold ionization spectrum.