  Based on first-principles calculations and symmetry-based indicator analysis,
we find a class of topological crystalline insulators (TCIs) with $C_2$
rotation anomaly in a family of Zintl compounds, including
$\mathrm{Ba}_{3}\mathrm{Cd}_{2}\mathrm{As}_{4}$,
$\mathrm{Ba}_{3}\mathrm{Zn}_{2}\mathrm{As}_{4}$ and
$\mathrm{Ba}_{3}\mathrm{Cd}_{2}\mathrm{Sb}_{4}$. The nontrivial band topology
protected by coexistence of $C_2$ rotation symmetry and time-reversal symmetry
$T$ leads to two surface Dirac cones at generic momenta on both top and bottom
surfaces perpendicular to the rotation axis. In addition, ($d-2$)-dimensional
helical hinge states are also protected along the hinge formed by two side
surfaces parallel with the rotation axis. We develop a method based on Wilson
loop technique to prove the existence of these surface Dirac cones due to $C_2$
anomaly and precisely locate them as demonstrated in studying these TCIs. The
helical hinge states are also calculated. Finally, we show that external strain
can be used to tune topological phase transitions among TCIs, strong Z$_2$
topological insulators and trivial insulators.
