Scott Manley did a video about this - turns out this is pretty energy intensive (asteroids are heavy & you are spinning up the whole thing) & not doable at all for many asteroid types due to insufficient material strength of the asteroid. Therefore, internal centrifuges in an asteroid cavern or spinning stations made from metal and/or advanced materials (wheels up to ONeil Island 3 design) are a much better bet than spinning asteroids.
Any artificial extrasolar objects that use spin for gravity would be far to small for current telescopes to resolve, not to mention detect their spin, if they are circular.
This is a cool idea. Maybe you could get the whole thing spinning and have really efficient gravity generation due to its mass.