Do you mean to use the table value of carbon atom polarizability (1.76 A^3, see ref.)?

Article Atomic and molecular polarizabilities

Polarizability arises from the McLaurin expansion of the total energy of a system in terms of the perturbation of an electric field. In fact, it is the second derivative of the energy with respect of the electric field component (the first one is the dipole moment, and the third, the first hyperpolarizability, and so on).

There is one iterative finite-field algorithm devised by Kurtz et al. (J. Comput. Chem 11, 82 (1990)), that you can also see in the reference attached, where it is applied to alkanes. I understand, though, it is not the only way to calculate it. In deMon2k it is pretty straightforward to calculate polarizabilities, as long as there is convergence of the self-consistent energy cycle.

Regards.

If you are able to solve the all-electron problem (with DFT, Hartree-Fock, etc.) you can use perturbation theory for the linear polarizability. This is somehow related with the random phase approximation as the zero frequency value of the response function.

Or, you can add in your Hamiltonian a stationary dipole field $\lambda z$, solve the DFT equations (with correct boundary conditions)  compute the total dipole moment and divide it by the strength of the external field $\lambda$. 

From the definition of the polarizability it should work.

if u r using gaussian software read the optimised carbon atoms output file u will find polarisablity of carbon .

1.  if u r unable to find do let me know i will send u the polarisablity of carbon.

2. plus r u talking about a single carbon atom or a molecule that comprises of carbon .send me its molecular formula and let me know that what basis set and functional  u r using . 

i hope ur querie is answered.