Chinese write it as 加, if you start making the strokes you get a + in the upper left. Consider this is over 6000 years old, probably the origin. My theory.

Edit (more evidence): "The plus symbol as an abbreviation for the Latin et, though appearing with the downward stroke not quite vertical, was found in a manuscript dated 1417 (Cajori)."

There is an assumption here that it's an abbreviation for the Latin et. But the downward stroke can be seen in the Chinese word.