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The concentration (in moles/volume) of CO2 in the ocean is higher than in the air, so it's not a bad idea.

One proposal was to do this electrolytically or by electrodialysis. This has been called "Direct Ocean Capture".

http://carbon.ycombinator.com/electro-geo-chemistry/

This may be considerably cheaper as a CO2 removal technology than DAC.

I had this thought too, an aqueous solution feels like it ought to be much easier to do chemistry with. But I haven’t heard of anyone working on it.

Here's a possible solution - add sodium to the fuel mix for cargo ships.

That's massively simplified, but this video gives more information and there are plenty of engineering challenges to overcome - https://www.youtube.com/watch?v=hL3AZGw9xZM

Been a while since I read up on this, but I think the problem is the energy cost of extracting CO2 from sea water makes it a wash at least in terms of CO2 reduction.