It's haunted. Really.
That sounds like the fill valve allowing a little bit of water through. This happens when there is a slow leak at the flapper or a siphon down the overflow tube.
Do this: Open the lid. Turn off the water at the wall. DO NOT FLUSH IT. Instead, mark the water level with a pencil. Let it sit, say, 4 hours or more. Go back. Open the lid. Has the water level dropped? If so, there's a slow leak, most likely at the flapper, and the fill valve is turning on just a smidge to refill that water that's leaking out of the toilet. Take a picture of the toilet insides, or give us the model number or whatever, and we'll help you find a replacement flapper, which will cost you like $5 and will take ten minutes for even the least-handy person to install.
Report back after your mission.