[Scorch]

It could be your sling affecting your groups, or it could be your technique. 10/22 rifles have a few special quirks.
* As Harry suggested, there are two bolts that hod the barrel retainer, make sure they are tight. Many 10/22s come from the factory with the barrel shank fitting the receiver very loosely, the barrel gets forced into a wedged position by the stock, and sling pressure can affect your point of impact and group size as it relaxes that pressure.
* 10/22s have only 1 action screw, and the receivers kind of teeter-totter inside the stock on that screw if you free-float the barrel. In order to cure this, you can bed the action and 1" of the barrel, then free-float the rest of the barrel (easy to do), or you can cross-drill the receiver and put in screws that hold the back of the receiver to the stock (harder to do), or you can do both (best solution). I cross-drill and bed the 10/22s I build, and they shoot quite well, but the cross-drilling should be done by someone who knows what they are doing.