Disassemble the shutoff valve—leaving the toilet and supply lines intact—then clean and flex the old neoprene washers inside the valve to renew them. Turn off the house water main before taking apart the toilet shutoff valve. Properly sized replacement washers for the shutoff valve are available from plumbing supply houses and better hardware stores that stock a large inventory of repair parts. If this step doesn't stop the leak, you'll need to replace the whole valve.
The plumbing supply shutoff valves behind toilets or under sinks can go for years without being turned off and then reopened again. That inactivity can cause the neoprene washers to become either brittle or crusted up with mineral deposits, and they lose their ability to seal leaks.
Occasionally, after shutting off a toilet supply valve to replace the tank plumbing parts, you may find that the shutoff valve leaks through the packing nut once the valve is opened again. To remedy this, most plumbing pros advise first using a groove joint pliers to tighten the packing nut one-eighth turn clockwise (Photo 1). If the neoprene washers are still flexible and clean, this should work to stop the leak.
If the leak persists, before replacing the entire valve, try this. Turn off the water at the house's main shutoff, then disassemble the problematic shutoff valve without disconnecting the valve from either the water supply line or the line leading to the toilet. Unscrew the handle, the packing nut and the threaded valve stem (Photo 2).
Clean the washers with a cloth and flex the neoprene to try to get it supple again. Avoid gumming up the inside of the shutoff valve; don't use any pipe dope or plastic tape on the valve stem's threads. Reassemble the shutoff valve, turn the main house valve back on and check for leaks. If the valve leak persists, turn off the main water shutoff valve, then disconnect the valve and replace it.