We investigated theoretically and experimentally the ultrafast birefringence induced by impulsive alignment in a molecular gas during optical filamentation. This phenomenon is able to substantially affect the polarization state of an ultrashort laser pulse that propagates through the aligned medium at suitable delays from a first aligning pulse. We exploited this modulation of the polarization state in order to effectively control the high-order harmonic generation (HHG) process, which is strongly dependent on the driving pulse polarization. These results open new and fascinating perspectives for the tailoring of strong-field phenomena by means of polarization pulse shaping.