Towards the end of The Bourne Legacy, he is shot in the leg by LARX #3. Later it shows blood on the shoulder of his jacket. I have watched this movie 30 times and have never seen him take a bullet to the shoulder...
Short answer: Yes.
Unlike the leg shot it isn't explicitly shown (or was edited out). LARX #3 fires three shots as Aaron flies past at the end of the street. The third shot hits him in the leg, so, from the angles it must have been the first shot that just grazed his left shoulder. If you look closely you can see his jacket being slightly ripped-up shortly afterwards, just before he spins his bike around.
It's the shoulder wound that causes Aaron to drop his gun after wounding LARX #3, and it also explains the shoulder bandage he's wearing on the boat as they sail away.
I went back to the last scene of the movie. Aaron's left shoulder is bandaged, supporting the claim he had also been shot it the shoulder.