One of four things (that I can think of...I'm not a pro)...either the fill valve in the toilet needs service - maybe just a new washer or gasket, or the float that turns the toilet on is sticking, or the shutoff valve's washer is deteriorated and plugging up the valve, or the hose/pipe between the toilet and shutoff is partially plugged.
How does the valve feel when you turn it off? Is it really spongy? get a bucket, turn the water off to the toilet, flush it and hold the lever down so all of the water goes out. Remove the pipe or hose that goes into the fill valve assembly in the toilet, get your bucket in place, then turn the water back on. Does it run? If it is not running well, then replace the hose/pipe between the shutoff and the toilet and try again. If it still is slow, shut off the main water, remove the toilet's shut off and get yourself a nice 1/4 turn shutoff and then put it all back together.
The hose could be swollen and full of crud as the result of high chlorine levels, or iron particles from galvanized piping, or other things. Shutting off then turning on the valve jolts things a little so it will run. My unprofessional opinion.