Well, kind of. The original stuff was just a castable plastic that turned out to be a really nice glue. There are formulations that were specifically for skin bonding, however.

What you can generally purchase as "superglue" (usually 100% ethyl or a blend of ethyl/methyl cyanoacrylate) is not the same thing as liquid stitches (Butyl or Octal cyanoacrylate), and only barely bonds to human skin (you can peel your fingers apart if you superglue them together, for example). The real medical-grade stuff is intense and fairly dangerous, as it can't be peeled off like people are used to and trying to remove it usually results in ripping patches off the skin.

You can sometimes get the real stuff (Dermabond is the most commonly available brand name) but it's so incredibly frequently counterfeited that buying from a reputable reseller is pretty critical if you don't want to put dirty unsanitized ethyl cyanoacrylate directly into an open wound. I've never found the real stuff on, for example, amazon.