This is because of its physico-chemical properties - CH3CN is a polar aprotic solvent with high dielectric constant (38.8) and dipole moment of 3.92 D thus capable of dissolving a wide range of ionic and non-polar compounds. Several of the monomers (nucleotides) used for the synthesis of oligonucleotides contain polar functional groups thus easily dissolve in CH3CN.
Anhydrous acetonitrile: acetonitrile is a good solvent for nucleophilic displacement reactions and anhydrous to prevent any competing hydrolysis reaction. See