  We examine the capability of pulsar timing arrays (PTAs) to detect very
small-scale clumps of dark matter (DM), which are a natural outcome of the
standard cold dark matter (CDM) paradigm. A clump streaming near the Earth or a
pulsar induces an impulsive acceleration to encode residuals on pulsar timing
data. We show that, assuming the standard abundance of DM clumps predicted by
the CDM model, small-scale DM clumps with masses from $\sim 10^{-11} M_\odot$
to $\sim 10^{-8} \ M_\odot$ can be detectable by a PTA observation for a few
decades with ${\cal O}(100)$ of pulsars with a timing noise of ${\cal O}(10)$
ns located at $\gtrsim 3$ kpc away from the Galactic center, as long as these
mass scales are larger than the cutoff scale of the halo mass function that is
determined by the particle nature of DM. Our result suggests that PTAs can
provide a unique opportunity for testing one of the most fundamental
predictions of the CDM paradigm. In addition, the detections and non-detections
can constrain the cutoff mass scale inherent to the DM model.
