We demonstrate the existence of a non-local geometric phase in the intensity-intensity correlations of classical incoherent light, that is not seen in the lower-order correlations. This two-photon Pancharatnam phase was observed and modulated in a Mach-Zehnder interferometer. Using acousto-optic interaction, independent phase noise was introduced to light in the two arms of the interferometer to create two independent incoherent classical sources from laser light. The experiment is the classical optical analogue of the multi-particle Aharonov-Bohm effect. As the trajectory of light over the Poincaré sphere introduces a phase shift observable only in the intensity-intensity correlation, it provides a means of deflecting the two-photon wavefront, while having no effect on single photons.