Wordorigins.org

A southpaw is a left-hander or the left hand. Today, the word is primarily used in baseball, but appears in other contexts as well. All we can say about the origin is that it is an unsatisfying “unknown.”

The earliest known use is in a political cartoon from 1848 titled Democratic B-Hoy (boy). The cartoon depicts Democratic presidential candidate Lewis Cass in a brawl with Zachary Taylor and a number of other Whigs. In the cartoon Cass is winning the fight, although in actuality he lost the election to Taylor. One of the Whigs who has been knocked to the ground says:

Curse the Old Hoss, what a south paw he has given me!

It is commonly claimed that the word originated in baseball slang, although given the quote above it is clear that boxing is a more likely source. The most common baseball explanation is that baseball diamonds were often arranged so the batters would face east, to avoid looking into the afternoon sun. The pitcher’s left hand, or paw, would therefore be on the southern side. Studies of late 19th century ball parks confirm this orientation, but use of the word southpaw in reference to baseball is not known prior to 1885. So the dates do not work. From Sporting Life of 14 January 1885:

They had always been accustomed to having their opponents hug their bases pretty close, out of respect for Morris’ quick throw over to first with that south-paw of his.

(Sources: Oxford English Dictionary, 2nd Edition; New Dickson Baseball Dictionary)