This paper presents the first study of static polarizabilities and polarizability anisotropies of copper clusters up to nine atoms calculated in the framework of density functional theory. The calculations were of all-electron type and have been performed by using a finite field approach implemented in the density functional program A LLCHEM. A newly developed first-order field induced copper basis set for density functional calculation was employed. A gradient-corrected exchange-correlation functional has been used. All cluster structures were fully optimized. The calculated polarizabilities of copper clusters are compared with experimental polarizabilities of sodium and lithium clusters. This comparison shows that the size dependency of the static polarizabilities per atom of copper clusters posseses the same trend as that observed in sodium clusters. However, the absolute polarizabilities of the copper clusters are considerably smaller as those of the sodium clusters.