Gravitational waves at suitable frequencies can resonantly interact with a binary system, inducing changes to its orbit. A stochastic gravitational-wave background causes the orbital elements of the binary to execute a classic random walk, with the variance of orbital elements growing with time.The lack of such a random walk in binaries that have been monitored with high precision over long time-scales can thus be used to place an upper bound on the gravitational-wave background. Using periastron time data from the Hulse-Taylor binary pulsar spanning ∼ 30 years, we obtain a bound of hc < 7.9 × 10 −14 at ∼ 10 −4 Hz, where hc is the strain amplitude per logarithmic frequency interval. Our constraint complements those from pulsar timing arrays, which probe much lower frequencies, and ground-based gravitational-wave observations, which probe much higher frequencies. Interesting sources in our frequency band, which overlaps the lower sensitive frequencies of proposed spacebased observatories, include white-dwarf/supermassive black-hole binaries in the early/late stages of inspiral, and TeV scale preheating or phase transitions. The bound improves as (time span) −2 and (sampling rate) −1/2 . The Hulse-Taylor constraint can be improved to ∼ 3.8 × 10 −15 with a suitable observational campaign over the next decade. Our approach can also be applied to other binaries, including (with suitable care) the Earth-Moon system, to obtain constraints at different frequencies. The observation of additional binary pulsars with the SKA could reach a sensitivity of hc ∼ 3 × 10 −17 .