The geometric phase in the beat signal from coherent interference of two frequency-offset light beams is measured using a novel distributed optical fiber sensing setup. In a fiber optic medium, with changing beam intensities, to the best of our knowledge, ours is the first measurement of the mentioned geometric phase. Experimental results of applying a 100-Hz sinusoidal stimulus to a polarization scrambler and a piezoelectric transducer inline to an optical fiber are presented. The results may enable novel distributed fiber sensing techniques.