Yes of course it is soluble.

For example the oceans are constantly getting $\ce{CO2}$ from atmosphere that gets converted into carbonic acid and thus increasing pH on global scale. Or the soft drinks we drink contain carbonic acid in them in dissolved form only due to mixing of $\ce{CO2}$ gas.

Also not all carbonates are insoluble as [Ben Norris](http://chemistry.stackexchange.com/questions/6587/is-h2co3-carbonic-acid-soluble-or-insoluble-in-water/6604#comment9672_6587) has commented.