There is no Scythe weapon RAW
As the other answers have already pointed out, there are currently no stats for a Scythe weapon in any of the official products. It certainly isn't listed on the weapons table in PHB (p. 149).
A Glaive is a good approximation
The best way to introduce a Scythe that I've found is simply reskinning a Glaive. Other answers have suggested this, but I've actually done this in the past (see below). A Glaive is a heavy, two-handed weapon with 10 ft. reach, like how you would imagine a Scythe would be, and although typically farmers would wield Scythes as makeshift weapons, the martial weapon proficiency represents how unwieldy they would be without the proper training and practice. The d10 slashing damage also seems representative of the Scythe's large blade.
My players seemed to agree
As DM, I have had two separate players in two separate games ask me about having a Scythe. In both instances I offered them the option of reskinning a Glaive. It worked well for both of them (one was a Paladin, the other a Pact of the Blade Warlock).
The two-handed, heavy and reach properties, as well as the d10 slashing damaging, really made it "feel" like a large Scythe, but RAW, it was a Glaive, so there were no balance concerns whatsoever (for example, no one could use it with a shield, since that's not something the Glaive would allow either). The Paladin character even used it with Polearm Master, since it is actually a Glaive regarding the mechanics, and none of this caused any problems for us.