Step 1: Recall CT scanner generations.
\[
\begin{aligned}
\text{First generation} &\rightarrow \text{Translate--rotate},
\text{Second generation} &\rightarrow \text{Translate--rotate},
\text{Third generation} &\rightarrow \text{Rotate--rotate},
\text{Fourth generation} &\rightarrow \text{Rotating source with stationary detectors.}
\end{aligned}
\]
Step 2: Identify the third-generation motion.
Hence,
\[
\boxed{\text{Rotate--rotate motion}}
\]
is the correct answer.
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.