Step 1: Understand Rochow-M\"uller process.
This process is used for the industrial synthesis of organosilicon compounds, especially dimethyldichlorosilane
It involves the reaction of methyl chloride (CH$_3$Cl) with silicon
Step 2: Role of catalyst.
A metal catalyst is required to facilitate the reaction between silicon and methyl chloride
Step 3: Identify the catalyst.
Copper (Cu) is used as the catalyst in this processIt enhances the formation of (CH$_3$)$_2$SiCl$_2$ as the major product
Step 4: Conclusion.
\[
\boxed{\text{Cu}}
\]