We propose and experimentally demonstrate a single-mode fiber length and dispersion measurement system based on what we believe to be a novel frequency-shifted asymmetric Sagnac interferometer incorporating an acousto-optic modulator (AOM). By sweeping the driving frequency of the AOM, which is asymmetrically placed in the Sagnac loop, the optical length of the fiber can be determined by measuring the corresponding variation in the phase delay between the two counterpropagating light beams. Combined with a high-resolution data processing algorithm, this system yields a dynamic range from a few centimeters to 60 km (limited by our availability of long fibers) with a resolution of approximately 1 part per million for long fibers.