Arawn does not appear in the Disney film adaptation of The Chronicles of Prydain but his role is filled by that of the Horned King. Arawn is meant to be the "spirit" trapped within the Cauldron. He was replaced by the Horned King in film because the animators felt that people would like the Horned King better since he had horns (similar to Maleficent and Chernabog). However, Arawn did receive a part in the movie. During the prologue, the narrator talks about the history of the Black Cauldron and how Arawn came to become it.
As stated in the prologue: "Legend has it, in the mystic land of Prydain, there was once a king so cruel and so evil, that even the gods feared him. Since no prison could hold him, he was thrown alive in to a crucible of molten iron. There his demonic sprite was captured in the form of a great Black Cauldron.". As such, one could argue that Arawn is included in the movie as the unseen master that the Horned King serves, with Arawn's dark magic powering the Black Cauldron.
Arawn's face is apparently engraved upon the cauldron. At certain points in the movie, the face is illuminated. There are several signs that the Horned King once served under Arawn as he says that now the power shall return to this world. Another sign of his connection to Arawn is that while being sucked into the Black Cauldron, he shouts, "Nooooo, you will not have me!".