Concept:
Photosynthesis in C$_4$ plants differs from that in C$_3$ plants because the initial fixation of carbon dioxide occurs in mesophyll cells through a specialized pathway known as the Hatch-Slack pathway. This adaptation helps minimize photorespiration and increases photosynthetic efficiency under conditions of high temperature and intense sunlight.
In C$_4$ plants, the first stable carbon dioxide acceptor is not RuBP as in the Calvin cycle. Instead, a three-carbon compound called phosphoenol pyruvate (PEP) accepts carbon dioxide to form a four-carbon compound.
Step 1: Understand the first carbon fixation reaction.
In the mesophyll cells of C$_4$ plants, carbon dioxide combines with phosphoenol pyruvate (PEP) in the presence of the enzyme PEP carboxylase.
\[
PEP + CO_2 \rightarrow OAA
\]
Thus, PEP acts as the primary acceptor of carbon dioxide.
Step 2: Analyze the given options.
PGA is the first stable product of the Calvin cycle in C$_3$ plants and is not the primary CO$_2$ acceptor.
RuBP acts as the carbon dioxide acceptor in the Calvin cycle but not during the initial fixation step of the C$_4$ pathway.
PEP is the actual initial carbon dioxide acceptor in C$_4$ plants.
PGAL is a three-carbon sugar produced during later stages of photosynthesis and does not function as a carbon dioxide acceptor.
Step 3: Draw the conclusion.
Therefore, the primary carbon dioxide acceptor in C$_4$ plants is phosphoenol pyruvate.
\[
\boxed{\text{PEP}}
\]
Hence, the correct answer is
\[
\boxed{(C)\ \text{PEP}}
\]