I have a leaky outdoor anti-siphon faucet. Unlike all the other outdoor faucets, it is apparently not connected to the main water shut off for the rest of the house. Is this common? Do I need to call the city to come out and turn off the water from the street or can a plummer do it?

You can close your incoming water supply at the curb, at the water meter. Once closed, your entire property will have no water.

Yes, sometimes we see hose valve attached before the house manifold and directly from the main.

You can close it yourself. You will need a large meter key to close it. Ask around, maybe one of your neighbor's have one and let you use it. Or, you can buy one in Home Depot.