Both State and Federal law place restrictions on individuals who have been convicted of felonies from possessing firearms. Oregon law also has a list of other weapons individuals who have been convicted of felonies cannot possess.
An "air rifle," assuming you mean something that uses compressed air to fire a projectile, is not a firearm according to Oregon law. See ORS 166.210(3). Nor is an air rifle one of the weapons listed under ORS 166.270 as a weapon prohibited to felons.
Federal law also prohibits individuals who have been convicted of a felony from possessing firearms. Federal law, for this purpose, defines a firearm as expelling a projectile by force of an explosive. An air rifle using compressed air is not using an explosive. However, if the air rifle is manufactured with frames or receivers of actual firearms, then it is prohibited.
Without more information about the air rifle in question, no definite answer can be given to your question. However, if the felony you have been convicted of is over 10 years old, you may be able to have it set aside or have your firearm rights restored. You should consult with an attorney in your area.
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