Barrel in hand, look at the index of the barrel extension pin, to the index of the FSB.  
If both are on the same plain TDC of the barrel together, then it may not be the barrel the problem, but when you where tightening the barrel nut, and it caused the barrel extension to slip in the upper receiver socket, and caused the entire barrel to be cant rotated in the upper receiver isntead.

If the upper barrel socket was peen larger, the sliver shim off a coke can is enough to keep the barrel extension pin tight in the upper receiver barrel socket slot to hold the barrel in the correct index as you tighten the barrel nut.



If the barrel extension pin to FSB is not the same index, then double check the FSB since it may not be taper pinned in place/adjustable isntead, and just a matter of installing the barrel with the barrel gas port TDC, then adjusting the FSB via live fire at the range to zero the rifle with the rear sight set dead center.

If the pin and FSB are not indexed correctly with the FSB taper pin installed, then still not the end of the world, since the Old FSB can be removed, and a clamp type FSB installed that will allow it to be adjustable on the barrel instead. Hence if you bought a used barrel and there is not option of sending it back to get a replacement barrel, this allows you to save the barrel, isntead of turning it into a tomato stake instead.

Also to note, if you want to see if the barrel did slip rotate in the upper barrel socket when the barrel nut was being tightened without having to remove the barrel, just compare the barrel extension lugs to the gas tube  and center line of the lower receiver front take down lug.  The center line of the top lug and the bottom lug (between the feed lips) should be straight up and down in the receiver.


Few last things, and on some upper receivers, the face of the upper barrel socket may not be square with the center of the bore line, you could have crap between it and the face of the barrel extension rim face to cause the barrel to be off center line of the upper receiver, could have bent the upper receiver barrel socket by using too much torque on the barrel nut to index it's top spline void with the gas tube channel  (don't go over 80ftlbs), or the barrel could be bent itself.