  Ultra-light Dark Matter (ULDM) models are suitable candidates for the
cosmological Dark Matter that may leave characteristic imprints in many
observables. Among other probes, signatures of ULDM can be searched for in
pulsar timing data. In this work we describe the effects of spin-2 ULDM on
pulsar timing arrays, extending previous results on lower spins. Spin-2 ULDM is
universally coupled to standard matter with dimensionless strength $\alpha$. We
estimate that current data could constrain this coupling in the mass range
$m\lesssim4\times10^{-22}$ eV at the $10^{-5}$ to $10^{-6}$ level, which is the
most competitive constraint in this mass range. A crucial feature of the spin-2
ULDM effect on pulsar timing is its anisotropic, quadrupolar shape. This
feature can be instrumental in differentiating the effects sourced by spin-2
ULDM from, for instance, scalar ULDM, and the systematics of a PTA experiment.
