Do I need to replace the anti-siphon valve?
That's a hose bibb vacuum breaker that's doing that, and it's shot
What you have there is a conventional hose bibb (outdoor faucet) that's been retrofitted with a hose bibb vacuum breaker to prevent a water main break from sucking whatever you left your garden hose in into the city's water system.  Unfortunately, with most of these retrofit-type devices, you need to drain them manually in order to winterize them, and if you don't, they may break, as yours clearly has.  You'll need to find and drill out the locking setscrew that holds yours on, then remove it and replace it with a new hose bibb vacuum breaker -- they're available at any hardware store.