Using numerical simulations of the magnetized solar photosphere carried out with the radiative magneto-hydrodynamic code, MURaM, and detailed spectro-polarimetric diagnostics of the simulated photospheric 6302 Å Fe I line, spectro-polarimetric signatures of Alfvén waves in magnetized intergranular lanes of the simulated solar photosphere were analysed at different positions at the solar disk. The torsional Alfvén waves in the intergranular lanes are horizontal plasma motions, which do not have a thermal perturbation counterpart. We find signatures of Alfvén waves as small-scale line profile Doppler shifts and Stokes-V area asymmetry enhancements in the simulated off-disk centre observations. These photospheric features disappear when the simulated observations are degraded with a telescope point spread function (PSF) similar to the one of Hinode. We analyse the possibilities for direct observations and confirmation of Alfvén wave presence in the solar photosphere.