I would like to know how many day will it take to get US from South Korea. Before asking, I check in google and other websites. But, I didn't find any answers. Could anyone guess me how many days it would take roughly to get US from South Korea.
EDITED: I can't delete this one as it has been accepted but a newer answer has more details, be sure to check it out!
I saw a journey from Seattle to Pusan in 19 days and from Vancouver to Pusan in 14 days so that should give you a ballpark figure for the time it takes to cross the Pacific ocean nowadays (albeit in the other direction).
Here are a few specific trips in the direction you asked about:
Both of these start from China because all the ships I could find either go to China before returning to the US and/or do not allow passengers to embark (but only to disembark) in South Korea. I don't know whether that's a general rule, you would have to contact an agent specialising in this to find out.
It is presently not possible to travel from S Korea to the US, or anywhere else, via freighter. Since the Sewol sinking, Korea has restricted embarkation for passengers on freighters, as reported to me by 4 different cargo travel agencies as of April 2016. I'm presently awaiting a CMA CGM vessel in Hong Kong, which was the next closest option. Ironically, we will be in Busan to load and offload cargo, though I am not permitted to leave the ship in that particular port. From Busan, that leg of the Columbus Loop is 12-14 days to Seattle, depending. Other ships on the Pearl River Express make a similar crossing to Long Beach, CA in about 12 days.
I've had excellent luck directing specific enquiries to Hamish Jamieson of Freighter Travel NZ, who's operated these sorts of voyages for quite a number of years.