Use an anti-siphon valve repair kit by turning off the house's water supply, disassembling the entire anti-siphon valve, and replacing all the old gaskets and o-rings in the valve with the new parts from the kit. Once you replace all the gaskets, reassemble the valve, remembering not to over-tighten the bolts, as this can damage the brand new gaskets and o-rings. Turn the water supply back on and check the anti-siphon valve for leaks.
If the anti-siphon valve still leaks after replacing every gasket and o-ring included with the repair kit, the valve is probably cracked or broken. Anti-siphon valves sometimes crack during hard freezes, when pressure from thawing water causes the valve walls to rupture. Unfortunately, fixing a cracked anti-siphon valve requires replacing the entire component, as repairs are not possible.
To replace an anti-siphon valve, turn off the water supply and use a hacksaw to cut through the PVC pipe that connects the anti-siphon valve to the sprinkler system. With the old valve removed, coat the threads of a male PVC adapter in Teflon tape and screw it into the new anti-siphon valve. Place the new valve exactly in the same location as the old one, as improper placement can cause the valve to malfunction. Using PVC cement, glue the new valve assembly into the sprinkler system, turn the water back on, and check for leaks.