We report polarimetric measurements of geometric phases that are generated by evolving polarized photons along nongeodesic trajectories on the Poincaré sphere. The core of our polarimetric array consists of seven wave plates that are traversed by a single-photon beam. With this array, any SU(2) transformation can be realized. By exploiting the gauge invariance of geometric phases under U(1) local transformations, we nullify the dynamical contribution to the total phase, thereby making the latter coincide with the geometric phase. We demonstrate our arrangement to be insensitive to various sources of noise entering it. This makes the single-beam, polarimetric array a promising, versatile tool for testing robustness of geometric phases against noise. © 2014 American Physical Society.