Covalent functionalization of a $B_{12}N_{12}$ nano-cage with $CO_2$ molecule has been investigated using density functional theory in terms of energetic, geometric, and electronic property analyses. Results show that besides two physisorption configurations, $CO_2$ preferably tends to perform [2+2] addition on B-N bonds of the cluster which are shared between six-membered and four-membered rings, releasing energy of 14.99 kcal/mol for adsorption of the first $CO_2$ and of 15.45 kcal/mol for the second one (per each molecule). On the basis of calculated density of states, we have found that the electronic properties of the physisorbed $B_{12}N_{12}$ by $CO_2$ have not changed, while slight changes have been predicted in the functionalized cases. Present results might be helpful to provide an effective way to modify the $B_{12}N_{12}$ properties for further purifications and applications.