Fiber transfer delay (FTD) variations influence the coherence of distributed radars with fiber networks, resulting in a performance degradation in target detecting and imaging. To measure and compensate for the variation, a phase-derived ranging based FTD measurement using a composite signal is proposed. The composite signal comprises a sinusoidal component and a linear frequency modulation (LFM) component. As the composite signal passes through a fiber under test (FUT), the sinusoidal component generates a phase shift that corresponds to the FTD. The phase shift can be represented by two parameters: the number of complete periods of 2π that can be estimated by using the LFM component, and a phase shift less than 2π that be measured employing the sinusoidal component. When using the proposed measurement system to measure FTD variations in a distributed radar, only an additional sinusoidal component is needed, which minimizes interference with radar signals. Moreover, the proposed measurement system can share core function modules such as signal generation and process modules with distributed radars, which enhances the compatibility and reduces the overall complexity. Experiments are carried out to measure a variable optical delay line and a long optical fiber. The experiment results verify the feasibility of the measurement system and show that a measurement range of more than 15 km, an accuracy of ±0.1 ps and a measurement time of 105 ms can be achieved.