Yes, Loki is indeed adopted. In the Marvel Universe, both in the comics and in the movie adaptations by Marvel Studios, Loki is the adopted son of Odin, the ruler of Asgard, and his wife Frigga. Loki's real father is Laufey, the king of the Frost Giants of Jotunheim. During a war between Asgard and Jotunheim, Odin defeated Laufey and found a small, abandoned baby in the wreckage. This baby was Loki, who was left to die due to his small size which is a disgrace in the eyes of the Frost Giants. Feeling a mix of sympathy and an opportunity for peace between the two realms, Odin decided to adopt Loki and raise him as his own alongside his biological son, Thor. This secret of Loki's true parentage leads to a lot of complications and shapes his character development throughout the series.