I thought he got it when he was younger and just became Jounin. This answer might have spoilers depending on where you're up to so read at your own risk xD lol
If you've watched "Kakashi's Gaiden" (episode 119&120 i think), he was on a mission during the third great war and him, Obito, Rin and Minato (4th hokage) were on a mission to destroy a bridge to prevent enemies or something but Rin was captured by a few enemies wanting information and Kakashi and Obito went to rescue her. While rescuing her, Kakashi's eye got slashed and he was blinded but then Obito who was crushed under a rock, gave Kakashi his eye which had the sharingan in it (Rin did the medical transplant).
The scar was most likely from when the enemy slashed his eye, and he would've lost an eye/being half blinded if Obito didn't give him his sharingan. Hope this answer helps :)
posted over a year ago
..u've got the perfect idea...i ave watched kakashi gaiden too...