  An ultralight free scalar field with mass around 10^{-23} - 10^{-22} eV is a
viable dark mater candidate, which can help to resolve some of the issues of
the cold dark matter 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. This frequency is in the range of pulsar timing array
observations. We estimate the magnitude of the pulse arrival time residuals
induced by the oscillating gravitational potential. We find that for a range of
dark matter masses, the scalar field dark matter signal is comparable to the
stochastic gravitational wave signal and can be detected by the planned SKA
pulsar timing array experiment.
