Calculated 13C NMR Shifts of brominated Carbons
The authors note in their review article* that such effects are expected as "heavy atom effects" due to electron-correlation effects and spin-orbit coupling: (references stripped for clarity)


  This being said, one way to improve the computed chemical shifts of heavy-atom-bound carbon atoms is to utilize a method that better captures electron correlation effects, such as MP2 or higher-level methods along with correlation-consistent basis sets (see section 4.3). This will likely result in significant improvement for carbon atoms attached to sulfur or phosphorus as well as to halogens, although the improvement is expected to be greater for sulfur or phosphorus. Further improvement requires the use of methods that determine relativistic spin–orbit corrections. 
  [...]
  
  Another option for improving chemical shift calculations with heavy-atom errors is to utilize a linear regression method, as discussed in section 3.6. Due to the systematic nature of heavy-atom effects, they are amenable to improvement via this approach, provided that the linear regression data consists of nuclei similar to the nucleus of interest. That is, a linear correlation correction to carbon nuclei attached to a given number of bromine atoms, for example, should be derived from empirical data for other carbon nuclei attached to the same number and type of halogen atoms. In fact, this approach has been demonstrated specifically for such cases.


The latter section cites two relevant articles:


"Theoretical investigation on $\ce{^1H}$ and $\ce{^13C}$ NMR chemical shifts of small alkanes and chloroalkanes" J. Chem. Phys. (2006) 125, 144309.
"A hybrid quantum mechanical and empirical model for the prediction of isotropic $\ce{^13C}$ shielding constants of organic molecules" Phys. Chem. Chem. Phys., 2002, 4, 5498-5507.


Both articles suggest ways to use DFT methods with empirical corrections that work fairly well.



* Michael W. Lodewyk, Matthew R. Siebert, and Dean J. Tantillo, Chem. Rev., 2012, 112 (3), 1839–1862.