  The recent discovery of gravitational waves from merging black holes has
generated interest in primordial black holes as a possible component of the
dark matter. In this paper, we show that pulsar timing may soon have sufficient
data to constrain $1$-$1000\,M_{\odot}$ primordial black holes via the
non-detection of a third-order Shapiro time delay as the black holes move
around the Galactic halo. We present the results of a Monte Carlo simulation
which suggests that future data from known pulsars may be capable of
constraining the PBH density more stringently than other existing methods in
the mass range ~1-30$\,M_{\odot}$. We find that timing new pulsars discovered
using the proposed Square Kilometre Array may constrain primordial black holes
in this mass range to comprise less than ~1-10% of the dark matter.
