Currently a way is lacking to detect unambiguously the possible phase coherence of an exciton condensate in an electron-hole double layer. Here we show that despite the fact that excitons are charge-neutral, the double layer exciton superfluid exhibits a diamagnetic response. In devices with specific circular geometry the magnetic flux threading between the layers must be quantized in units of $\frac{h}{e} \chi_m$ where $\chi_m$ is the diamagnetic susceptibility of the device. We discuss possible experimental realizations of the predicted unconventional flux quantization.