Diagnostic techniques for stellar magnetic fields based upon spectropolarimetry. We propose and explore a new technique based upon the linear polarization emitted in Hanle-sensitive lines in disk-integrated stars where a dipolar magnetic field breaks the rotational symmetry of the resonance scattering polarization. A star with a simple dipolar field and a 1-0 spectral line are used to compute polarization amplitudes and angles.Predicted amplitudes are low but within reach of present instruments. A new application of the Hanle effect is proposed and analyzed, a tool that allows measuring of some of the weakest stellar magnetic fields.