* "Suffragist" is a fairly short and straightforward word. Unlike longer terms, it doesn't need abbreviation.
* The movement was diverse. Different groups with varying goals and tactics existed. An acronym might not accurately represent all of them.
While there's no official acronym, you might encounter the term "suffragette" used informally. It's not technically an acronym, but it's a shortened form of "suffragist," often referring specifically to the more militant British women's suffrage movement.