Based on first-principles calculations and a symmetry-based indicator analysis, we find a class of topological crystalline insulators (TCIs) with a $C_2$ 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 the 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 to the rotation axis. We develop a method based on the nested Wilson loop technique to prove the existence of these surface Dirac cones due to a $C_2$ 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 the topological phase transitions among TCIs, strong $Z_2$ topological insulators, and trivial insulators.