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We present a novel method for aligning a laser ionized plasma source to a pair of ultra-relativistic electron beams that comprise a plasma wakefield accelerator (PWFA). We achieve alignment by analyzing the plasma afterglow light observed at two longitudinal locations as the plasma column is scanned across the electron beam. By analyzing the relative plasma light intensity at the two locations, we aligned an 85-cm plasma source to a 10 GeV, 1.6 nC electron beam to within 10 um offset, 10 urad tilt. The alignment is verified by analyzing the drive beam energy loss, energy transfer efficiency, and the witness beam energy gain as a function of the misalignment between the beams and the plasma. From this measurement, we extract the alignment tolerance required between the laser-ionized plasma source and electron beams, an important metric necessary for collider design studies or light source applications based on a laser-ionized plasma source.