The process of introducing a phosphate group on to an amino acid residue in the C-terminal domain of RNA polymerase II. Typically, this occurs during the transcription cycle and results in production of an RNA polymerase II enzyme where the carboxy-terminal domain (CTD) of the largest subunit is extensively phosphorylated, often referred to as hyperphosphorylated or the II(0) form. Specific types of phosphorylation within the CTD are usually associated with specific regions of genes, though there are exceptions. The phosphorylation state regulates the association of specific complexes such as the capping enzyme or 3'-RNA processing machinery to the elongating RNA polymerase complex.