I wipe it off with a rag then apply some Otis oil using a clean patch, I also run a Bore snake with a little otis oil on it through the barrel.
Chief
Just out of curiosity, have you ever asked yourself why (other than from habit) you are putting a light coat of oil on the inside of the barrel? In the case of the military weapons you have mentioned like M16's etc all the way up to the M2 50 Cal, they are all hard chrome lined or stellite lined. In the case of the Rohrbaugh it is stainless steel. I suspect this is how you, like I ,were trained, especially in the military. I'm pretty sure this is a hold over that the military has taught since before the days of chrome lined and stellite lined barrels and is a hold over from corrosive ammunition. In US ammunition the manufacture of military ammunition with corrosive priming compounds ended sometime in the mid 50's. The last commercial ammo that I personally know of that was loaded with corrosive priming in this country was some lots of 300 H&H that Olin loaded for the Wimbleton Cup around 1959.
The old cliche about "can't hurt, might help," doesn't apply here because in some cases it does. Long range shooters from Marine Scout Snipers to heavy competitive long range shooters have to have a bone dry barrel or else their zero will change after they fire 2 to 5 shots and the barrel is now bone dry and fouled. Hence the term "fouling shot". When I learned that during Police Rifle Instructor and Long Range Rifle Instructor programs, which were and are still taught by former members of the Marine MTU from Quantico, I quit doing it on all weapons period. If you like doing it then I'm all for you doing what winds your watch. All I say is, think about it for a minute.
I was taught to do the exact same thing by my father who was retired Army and in the military during my time in the 60's.
The only time I do it now is during periods of long term storage for weapons that do not have chrome lined or stainless barrels. In my M1A's for example the one with a GI barrel by Springfield has chrome lining. My National Match doesn't have chrome lining and I would oil it for storage but if I'm going to shoot it, no. My sniper rifles I never oil because I don't know when I might need them. I also store all my long guns muzzle down in my safe so that no oils accumulate in the stock area of those that have wooden stocks. That's why the old surplus military rifles stocks are all turning black around the metal is due to oil soaking and standing them in rifle racks butt down. Everywhere they are black the wood is soft and pulpy which is a deterent to accuracy.