In Soul Eater, does Soul ever become a death scythe? If so, which episode? I have heard rumors he only becomes a death scythe in the manga but it is still unclear. Has it just not happened yet in the anime?
No, in the anime of soul eater a death scythe is more of a conceptual goal than a visible state of progression, however, as the anime progresses a character who is an actual death scythe is introduced and it's power is displayed to reinforce that goal.

Keep in mind that the anime also ends at the internal investigation arc (chapters 38-40) as the Kishin arc - Arachnophobia vs DWMA - is anime only. I will leave out details if you haven't seen it to avoid spoilers but I do recommend watching it. 

My source is that I watched the anime fairly recently and recall the details.