No. The possessive of it is its. It's is the contraction of it was or it is. Similarly, the possessive of who is whose rather than who's. Who's is the contraction for who is or who has.
Its collar is leather with embedded diamonds. Possessive
We're all interested in whether it's (it is) possible. Contraction
The girl whose car was stolen is waiting outside. Possessive
Who's in charge of this activity? Contraction