Use ion chromatography.  See the United States EPA method.  Also see the Dionex website.

But in fact I determined the carbonate ion by ion chromatography the carbonate is compound not element ?

Yes.  Dionex has a method for cations and a separate method for anions (like Carbonate).  These methods were 1st used and strongly recommended by the EPA on surface waters.

Remember that carbonate is ion too, and like metal ions it can be determined by ionic chromatography

we can determine metal cations by Atomic Absorption spectrometer or using Ion selective electrode instead of chromatography method