" Depends". would be a important word here. Yes,it can be done BUT unless you have a chamber adapter for .22 magnum to .22 LR round it wont happen due to micro tolerances within the two .22 rounds. The .22 lR round will engage in the grooves[Just about] but dont expect sub MOA groupings from these rounds.
Some .22 mag rifles and handguns will accept .22lr" Sleeved rounds"[Ruger .22mag revolvers are famous for this].Simply a .22lr sleeved over with a .22 mag shell body with the end cut off.Others wont do it at all. My Savage.22mag/20 Ga will gobble any old dirt in ammo but chokes on this set up and it has some of the easiest tolerances in chamber dimensions.You will have to experiment with various different brands of 22mag ammo to see which works in your particular gun.IF at all!

Nor is it particulary wise to do it as some guns will give you powder blow back on firing the 22 lr in the magnum chamber.So it is really advisable to wear eye protection if you use this set up.
Best advice .
Buy a proper .22lr to .22mag chamber adapter
Wear saftey shooting glasses when firing.
Buy a .22 that will handle super hot .22lr loads.They are becoming better and deliver as much oomph these days as the .22 mag.