  Using first-principles calculations we predict that $\mathrm{TiRhAs}$, a
previously synthesized compound, is a Dirac nodal line (DNL) semimetal. The DNL
in this compound is found to be protected both by the combination of inversion
and time-reversal symmetry, and by a reflection symmetry, in the absence of
spin-orbit coupling (SOC). Our calculations show that band velocities
associated with the nodal line have a high degree of directional anisotropy,
with in-plane velocities $v_\perp$ perpendicular to the nodal line between
$1.2-2.8\times10^5$ m/s. The crossings along the DNL are further found to
exhibit a prominent and position-dependent tilt along directions perpendicular
to the nodal line. We calculate $\mathbb{Z}_2$ indices based on parity
eigenvalues at time-reversal invariant momenta and show that $\mathrm{TiRhAs}$
is topological. A tight-binding model fit from our first-principles
calculations demonstrates the existence of two-dimensional drumhead surface
states on the surface Brillouin zone. Based on the small gapping of the DNL
upon inclusion of SOC and the clean Fermi surface free from trivial bands,
$\mathrm{TiRhAs}$ is a promising candidate for further studies of the
properties of topological semimetals.
