It can, but not enough to physically hurt you. But:

It's not the kind of radiation that causes cancer. I'm going to really simplify things here, but when we think about radiation in this context, there's 2 kinds - ionizing and non-ionizing. Anything that's got a longer wavelength than UV light is non-ionizing. This is pretty much all of the stuff we find useful for everyday tech: cell phones, wifi, microwaves, and all that jazz.

Ionizing is the stuff that can hurt us, like UV, X-rays, and Gamma rays. We still have all kinds of useful tech that relies on that stuff, but aside from UVA blacklights, you won't often find it in your home.

Quick edit: microwaves and non ionizing radiation can still hurt you. Microwaves excite water molecules and can cause burns to tissues under your skin. Best to try to avoid exposure.