Bloodfang, published in British comic Eagle, issues 116–127 and 129–158 (1983–84).
The first series (12 episodes, 38 pages) begins with Bloodfang hatching from his egg, 100 million years ago. He promptly kills his siblings, and is raised by his mother, Karka, until she is killed in a fight with the tyrannosaur pack leader, Blackheart, who happens to be Bloodfang's father. During the fight Bloodfang is wounded in the face by Blackheart, leaving him with permanent scars. Bloodfang flees, and becomes an outcast from the pack.
Forced to fend for himself, the young tyrannosaur initially struggles to survive, and nearly starves. His first meal without his mother's assistance consists of carrion. However, when other dinosaurs (four sauroctoni) try to steal his meal from him, he cunningly bides his time until they have gorged themselves, and then attacks them when, sleepy and bloated, they are vulnerable, killing two and driving the others away. Over the next four years he grows to become six metres tall and weigh ten tonnes, by which time he has learned to be a ferocious fighter, stronger than most adults of his species.
Bloodfang returns to his pack during mating season, and kills a rival male tyrannosaur to steal his harem of females. Bloodfang quickly establishes his status as one of the strongest of the pack, but backs down when challenged by Blackheart, who is still the leader.
Eventually, during a final reckoning, Bloodfang kills Blackheart and usurps him as leader of the pack, while the rest of the pack feast on Blackheart's corpse.
The second series apparently involves Bloodfang dealing with hunters from the 22nd century.
Found by searching for comic young "tyrannosaurus rex" scars -"jurassic park"