You can join an affiliation when you reach Rep level 10. The game will automatically ask you to join once you reach level 10. You have two choices to pick from: The Hearts and The Clubs. Join one, and achievement pops. If it doesnt pop, try getting to where you can switch affiliations (defeat other affiliation boss). Switching might help this achievement pop.
The Spades unlock at level 25 and The Diamonds unlock at level 50.