Depends............
Do you have a three (3) screw Old Model, or a two (2) pin New Model Single Six ?
If it's an OM, call Ruger Cust Service with the SN, to find out if it's suitable as a convertible - IOW, is the barrel up to .22 Mag specs (pre-1959 Single Six's had .219" bbls ILO the later slightly larger bores.)
If it's a NM, or a suitable OM, measure the exact length of your .22LR cylinder's central arbor with a caliper - IOW, it's LOA.
When you buy a used .22 Mag cylinder:
1) Be sure it's the same model (New or Old) as your gun.
2) Be sure the prospective purchase's arbor is the same length or longer than your .22LR cylinder's.
(longer ones can be dressed down to fit, but short ones are difficult to stretch)
.