We investigate the feasibility of measuring line-of-sight magnetic field strength in the solar chromosphere through Stokes polarimetry in the hydrogen Hα line. Because of the large intrinsic Doppler width of the hydrogen line, the weak-field approximation applies even for the strongest magnetic fields in the solar atmosphere. We calculate the Hα response functions of Stokes I and V to perturbations in the magnetic field and temperature in two different one-dimensional solar models representing the average quiet Sun and a sunspot umbra. These response functions show that the Hα line exhibits large photospheric sensitivities in these solar models in addition to its chromospheric sensitivity. One particularly striking example is the Stokes V response in the quiet Sun, which is mostly photospheric when the field decreases with height.