Step 1: Covalent character in an ionic compound is explained by Fajans' rule. It depends on the polarizing power of the cation and the polarizability of the anion. A bigger, softer anion is polarized more easily, so the bond gains more covalent character.
Step 2: In all four compounds the cation is the same, \(Ca^{2+}\). So the covalent character depends only on the anion. Anion size increases as \(F^- \lt Cl^- \lt Br^- \lt I^-\), and polarizability increases in the same order.
Step 3: Since \(I^-\) is the largest and most easily polarized halide ion, \(CaI_2\) has the highest covalent character. \(CaF_2\), with the smallest and least polarizable \(F^-\), has the lowest covalent character.
So the order of covalent character is:
\[CaF_2 \lt CaCl_2 \lt CaBr_2 \lt CaI_2\]
\[\boxed{\text{Option (C)}}\]