The Warden Crossbow first becomes available during
Chapter 3. While speaking to O'Neal in his safe house, he will tell you about a crossbow next to an abandoned APC down the street (You don't need to hear this dialogue to get the crossbow). There will be a few lost in the surrounding area. When you get close, they will all walk away, allowing you to sneak around the left side of the APC to pick up the crossbow.
Here's my guide for all of the collectibles in the game, weapons included. You can skip to 5:10 for the Warden Crossbow.