Charcoal was used as a carbon source for improving the critical current density of $MgB_2$ and the effect of annealing temperature on the $J_c$ of $MgB_2$ was investigated. The charcoal powder used in this study was $1{sim}2$ microns in size and was prepared by wet attrition milling. $MgB_2$ bulk samples with a nominal composition of $Mg(B_{0.95}C_{0.05})_2$ were prepared by in situ process of Mg and B powders. The powder mixture was uniaxially compacted into pellets and heat treated at temperatures of $650^{circ}C;-;1000^{circ}C$ for 30 minutes in flowing Ar gas. It was found that superconducting transition temperature of $Mg(B_{0.95}C_{0.05})_2$ decreased by charcoal additions which indicates the carbon substitution for boron site. $J_c$ of $Mg(B_{0.95}C_{0.05})_2$ was lower than that of the undoped $MgB_2$ at the magnetic fields smaller than 4 Tesla, while it was higher than that of the undoped sample especially at the magnetic field higher than 4 T. High temperature annealing seems to be effective in increasing $J_c$ due to the enhanced carbon diffusion into boron sites.