Shit is a very old word, with an Old English root. *Scítan is the Old English word. It has cognates in most of the other Germanic languages and shares a common Germanic root with modern equivalents like the German scheissen.
*Scítan, however, doesn\'t appear in extant Old English texts and is only assumed to have existed in Old English. The verb to shit dates the Middle English period (c. 1308), and the noun form is from the 16th century. The interjection is of quite recent vintage, not found until the 1920s.
In 2002, an alleged acronymic origin for shit appeared on the Internet. According to this tale, the word is from an acronym for Ship High In Transit, referring to barges carrying manure. This is a complete fabrication and absurd on its face. All it takes to disprove it is to look up the word in any decent dictionary. Remember, anytime someone posits an acronymic word origin, chances are that it is utterly false.