Does Amir get an internal scar after witnessing the rape of Hassan?

Yes, you could say that Amir is "scarred" by witnessing his friend Hassan being raped. He is certainly traumatized by what he sees and also by his own lack of action: he stands outside the scene but does not intervene to help Hassan. Many readers condemn Amir's actions, but Khaled Hosseini also makes it clear that, despite his abominable actions toward Hassan, Amir also suffers as a result of the assault against Hassan.
After the scene in which Hassan is sexually assaulted in the alley, Amir is both utterly ashamed of himself and desperate to have his sins known. For example, one night when everyone is sleeping, Amir says, "I watched Hassan get raped," to no one (86). Amir says, "A part of me was hoping someone would wake up and hear, so I wouldn't have to live with this lie anymore" (86). Amir feels that it may be worse for no one to ever know what he did (or did not do): "I understood the nature of my new curse: I was going to get away with it" (86). Amir's desire to be punished for the wrong he has committed is also clear in the scene in which he throws pomegranates at Hassan and begs him to throw them back at him. After Amir throws the fruit at Hassan, he exclaims, "Get up! Hit me! . . . Hit me back! Hit me back, goddamn you!" (92). Hassan does not fulfill Amir's request and instead hits himself in the face with a pomegranate. We can also see Amir projecting his own guilt onto Hassan by calling him a coward in this scene. These examples suggest that Amir feels immense regret for what he has done and can only move past the incident if he faces appropriate consequences.
Amir, though, avoids Hassan and then manages to get him and Ali to leave Baba's house before Baba and Amir move to America—never to see their servants/friends again. As an adult, some twenty years later, Amir is still haunted by his actions and inaction; this is why he is so struck when Rahim Khan calls him and tells him, "There is a way to be good again" (2). Amir embarks on a redemptive quest that sees him overcome numerous obstacles to rescue and adopt Sohrab, Hassan's son. One of the most significant scenes involves Amir physically fighting Assef, Hassan's assailant and Sohrab's abuser, until Amir is nearly killed. In this fight, Amir acquires a symbolic physical scar. Amir recalls, "I kept thinking of something else Dr. Faruqi had said: "The impact had cut your upper lip in two . . . clean down the middle. Clean down the middle. Like a harelip" (297). This is significant because Hassan was born with a harelip, which Baba had a surgeon fix for Hassan's birthday one year. Amir now feels to some extent like Hassan, since he has been physically beaten by Assef and also carries a scar that will always remind him of Hassan. The fight also provides Amir with a sense of relief; he feels cleansed because he is finally being physically punished. Amir laughs while Assef punches him and explains, "My body was broken . . . but I felt healed. Healed at last. I laughed" (289). It seems symbolically appropriate, too, that Amir now has a physical scar to match his inner pain, and this scar also seems to help him externalize his guilt and venture beyond (or begin to) the sins of his childhood.