Who is Eric Cartman's half-brother?

Eric Cartman's half-brother is Scott Tenorman.

Scott is the son of Jack Tenorman, the former Denver Broncos player later revealed to be Cartman's biological father. Because Cartman and Scott share Jack as a father but have different mothers, Scott is Cartman's paternal half-brother.

Their relationship is introduced long before the family connection is known. In the season-five episode “Scott Tenorman Must Die,” Scott tricks Cartman in a pubic-hair scam. Cartman retaliates with an elaborate scheme that gets Scott's parents killed and turns them into chili, which Scott is manipulated into eating. The season-fourteen episode “201” then reveals that Jack was Cartman's father, giving the earlier episode a much darker meaning.

Scott is not merely another school rival or a distant relative. He is specifically Cartman's half-brother, although the two boys have one of the most hostile relationships in the series. The other listed choices belong to different South Park families and are unrelated to Cartman's parentage.