  In the paper, we calculate the fragmentation functions for $g \to B_c$ and $g
\to B_c^*$. The ultraviolet divergences in the calculation are removed through
the renormalization of the operator definition of the fragmentation functions
under the modified minimal subtraction scheme. We then obtain the fragmentation
functions $D_{g \to B_c}(z,\mu_F)$ and $D_{g \to B_c^*}(z,\mu_F)$, which are
presented as figures and fitting functions. The obtained fragmentation
functions are complementary to the previous work on the next-to-leading order
fragmentation functions for $\bar{b}\to B_c(B_c^*)$ and $c\to B_c(B_c^*)$.
