On D&DBeyond, I've found this homebrew Kuo-toa race. There are others, even on D&DByeond, but this is the one that seems to most closely adhere to how the Kuo-toa appear in the Monster Manual (or their D&DBeyond stat block).
I'll reproduce the racial traits and such here:
Otherworldly Perception
The kuo-toa can sense the presence of any creature within 30 feet of it that is invisible or on the Ethereal Plane. It can pinpoint such a creature that is moving.
Age
Kuo-Toa live slightly shorter lives in comparison to humans, maturing at the age of 7 and reaching ages up to 50.
Alignment
Kuo-Toa are mostly neutral or evil, and although they have a rigid sense of their own law, they may seem chaotic to other humanoids.
Size
Kuo-Toa reach are around 4-5 feet tall. Your size is medium.
Langauge
Kuo-Toa adventurers can speak, read, and write Common and Undercommon.
Ability Score Increase.
Your Wisdom score increases by 2 and your Constitution score increases by 1.
Amphibious
The Kuo-Toa can breathe air and water.
Slippery
The kuo-toa has advantage on ability checks and saving throws made to escape a grapple.
Sunlight Sensitivity
While in sunlight, the kuo-toa has disadvantage on attack rolls, as well as on Wisdom (Perception) checks that rely on sight.
Some of these details don't seem to have any source that I know of, such as their age range, but otherwise the mechanical aspects seems to honour the stat block of the "monster" kuo-toa.
But is it balanced compared to the other player races? In particular, the Otherworldly Perception trait looks to me like it might be overpowered, but would this make it overpowered compared to, say, the Yuan-ti Pureblood, which I believe is considered the most powerful of the monstrous races from Volo's Guide to Monsters?
In response to some answers; I didn't actually spot that this doesn't have a swim speed of 30 feet! I just assumed it would have (I mean, why wouldn't it? Of course it should)! If I were to make use of this, I would definitely ensure that it has a swim speed of 30 feet (I'm the DM in this situation).