The process of introducing a phosphate group onto a serine residue at position 2 within the heptapeptide repeat (YSPTSPS) of the C-terminal domain of RNA polymerase II. Typically, phosphorylation of serine 2 (Ser2) occurs subsequent to phosphorylation of serine 5 and is thus seen in the middle and 3' ends of genes. In vivo, Ser2 phosphorylation is primarily performed by CTDK-I in S. cerevisiae or CDK9 in metazoans.