  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 h_c < 7.9*10^(-14) at
~10^(-4) Hz, where h_c 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 space-based
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 h_c ~ 3*10^(-17).
