The barium strontium titannate ((Ba,Sr)TiO$_3$:BST) thin films were etched in an inductively coupled plasma (ICP) as a function of CF$_4$/Ar gas mixing ratio. Under CF$_4$(20%)/Ar(80%), the maximum etch rate of the BST films was 400 $AA$/min. Etching products were redeposited on the surface of BST and then the nature of crystallinity were varied. Therefore, we investigated the etched surface of BST by X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). The plasma damages were evaluated in terms of leakage current density by Agilent 4145C and dielectric constant by HP 4192 impedance analyzer. After the BST thin films exposed in the plasma, the leakage current density and roughness increases. After annealing at 600 $^{circ}C$ for 10 min in $O_2$ ambient, the leakage current density, roughness and nonvolatile etch byproducts reduced. From this results, the plasma induced damages were recovered by annealing process owing to the relaxation of lattice mismatches by Ar ions and the desorption of metal fluorides in high temperature.