Yep - but, depending upon the present bbl's muzzle OD, a rebore should suffice (much less expensive than a rebarrel).
Most reborers won't rebore a barrel to whatever ID/caliber unless the end result leaves a bbl thickness (NOT O.D.) of at least .125" @ the muzzle.
Which means that your .22/250 bbl's muzzle OD cannot be less than .550", in order to accept a rebore to .308".
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