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.
In the anime no, however know that the anime does not follow the manga entirely, as Hikari points out
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.
is when the anime deviates from the manga as in the manga near the end
Crona ends up becoming a Kishin and flees to the Moon with an army of clowns similar to the 2 clowns that Kid faced in the anime when he went to obtain the last of Ebion's Tools needed for Death
i havn't read the manga so i don't know exactly when but on Soul's Synopsis Wikia Page under Formation, partway though the second paragraph it says
Spirit hands Soul Arachne's Witch soul and congratulates him on becoming a Death Weapon. The other members of Spartoi join them, as Soul, drooling and with a smirk on his face, consumes Arachne's soul and becomes a Death Weapon, signaling the birth of the elite student group, Spartoi.
Well, the anime very greatly deviates from the manga. In fact, only less than the first half of the anime follows the manga. The rest is completely different. Considering the events of the manga: (SPOILERS)
Soul becomes death scythe after some time after the events of the Baba Yaga castle by killing a witch. Comparing it with the anime, they had to confront the Kishin right after attacking the Baba Yaga castle and the anime ended eventually. So I don't think Soul ever became a death scythe in the anime. He does become a death scythe in the manga in chapter 62.