Would it be possible to spin a ball in a space station, and for it to create its own orbit for a smaller ball to rotate around it?
As PM 2Ring mentioned, you seem to have a misunderstanding that spin is involved in creating an orbit. What matters for gravitational attraction is the mass of the bodies and their distance, the effects of spin are more subtle and only an issue when bodies are non-spherical. Also, one body doesn't need to be smaller than the other, they can be the same size.
A lead sphere 10 cm across would mass 6 kg. If two such spheres were 10 cm apart (20 cm center-to-center), they would have a gravitational pull on each other of 0.06 micronewtons...not nearly enough force to feel. They would technically have an orbital period of about 5.5 hours, with an orbital velocity of a few millimeters per minute, but pretty much any random air current would blow them out of orbit and no human could place them precisely enough in the first place, and nearby masses (like the humans occupying the station) would throw them off.