Hong named the Borussia Monchengladbach midfielder in his 26-man squad on Monday as the Koreans begin preparations for next year's World Cup, their 11th consecutive appearance in the global tournament.
The 22-year-old Castrop, who was born to a German father and South Korean mother, has been picked along with captain Son Heung-Min and Paris Saint-Germain's Champions League winner Lee Kang-In.
Castrop, who was born in Dusseldorf and played for Germany from Under-16 to Under-21 level, asked FIFA to switch his international allegiance to South Korea this month.
He played for Koln and Nurnberg before joining Monchengladbach in February.
While selecting overseas-born players has become commonplace in China and Japan, in South Korea it is rare at all levels of the sport.
Striker Casey Phair became the first mixed heritage player to be selected for South Korea at senior level in 2023 when she represented the country in the Women's World Cup.