The word is Qashata (pronounced Qash-shaa-ta). The "Q" represents the 19'th letter of the Aramaic alphabet. The rest is self-explanatory.
I would imagine the word is the same as in the time of ancient Assyria since it is related to the Aramaic word for bow, Qishta. If I'm understanding your question correctly, you're not asking for the Akkadian word for "Archer" since that was a language also spoken in ancient Assyria, right?
Edit: Aturaya, I corrected myself. In the word "Qashata", the second to last letter is a Taw and not a Teith. When I sounded the word out, I heard the right sound but somehow I visualized something else. I'm surprised nobody caught my mistake. Or they were being too nice by not pointing it out. Hopefully I got it right this time.