Yes there is a crossbow in the game. I myself have unlocked it through raising my Local Influence in the game,, and believe it or not there is also a repeating crossbow when you reach max LI. It is an awesome weapon to use and has the most range out of all the secondary weapons.
I love how in the other forum topics everyone wants the next socom so real and more like life then they go and put a crossbow in the game? I may not be a navy seal or in the army but I don't think they use that.