An ultra-light free scalar field with mass in the range 10^{-23} - 10^{-22} eV is a viable dark mater candidate. It can address the overabundance of cold dark matter structures on sub-galactic scales. We consider the gravitational field of the galactic halo composed out of such dark matter. The scalar field has oscillating in time pressure, which induces oscillations of gravitational potential with amplitude of the order of 10^{-15} and frequency in the nanohertz range. We find that for a range of dark matter masses, the scalar field dark matter signal is comparable to the expected stochastic gravitational wave signal and could be detected by the planned SKA pulsar timing array experiment.