Jim Sanders is an aspiring composer who is engaged to Patty Winston, the spoiled daughter of cosmetics-company owner Ed Winston. On the night of the engagement party, three masked robbers kidnap Jim and escape in a car. The kidnappers turn out to be Jim's best friends, George, Don, and Rex, who drive him back to his apartment for his bachelor party. Later, after Jim passes out drunk, he awakens to find an Angel lying unconscious in his swimming pool. He revives her with mouth-to-mouth resuscitation. The Angel cannot speak, only communicating in coos and high-pitched squeals. As they discover that her right wing is broken, she kisses Jim.
The next morning, George, Don, and Rex discover the Angel at Jim's apartment and propose exploiting her for profit, but Jim opposes it. Shortly after Jim sews up the Angel's broken wing, Patty Winston arrives at his apartment, but seeing the Angel wrapped in a blanket, she assumes Jim is having an affair and leaves in anger. That night, he takes the Angel to a fast-food restaurant, where she develops a taste for French fries. While Jim leaves to call Patty from a payphone, unsuccessfully trying to make amends, his friends attempt to lure the Angel into their car with French fries, before he chases them away and takes her back home. There, Ed Winston arrives and confronts Jim, but upon looking at the Angel's face, he becomes enchanted by her and leaves.
The next day, due to the failure of his company's latest campaign, Ed sets out to replace Patty with the Angel as the company's spokesperson, which further infuriates Patty. Meanwhile, Jim's friends devise a scheme to capture the Angel by arranging for him to meet Patty over a reconciliation. When Jim arrives with the Angel, Patty storms out and he follows, whereupon his friends kidnap the Angel and drive away. The next day, as the trio reveals a bound and gagged Angel to a press conference, Jim comes to her rescue and takes her to his old treehouse in the woods.
While hiding out, Jim tells the Angel that his father got him interested in music, but six months earlier, he began to suffer from severe headaches that caused him to stop composing. Jim and the Angel then share a dance to one of his compositions. After removing the bandage from the Angel's wing, Jim advises her to leave before the others find her. As the Angel disappears, an increasingly unhinged Patty arrives and slaps Jim, prompting an invisible Angel to punch and kick Patty. Ed and Jim's parents arrive, as do George, Don, and Rex. Amid the chaos, the Angel reappears and drives away Patty and Ed with rain clouds, before disappearing into the sky.
The others notice that Jim has collapsed and rush him to a hospital, where the doctor reveals that his headaches are caused by a brain tumor in an advanced stage. When the Angel appears in Jim's hospital room, he is convinced that she has come to take him to heaven. She kisses him, and as he falls asleep, she wraps her wings around him. Shortly after, George, Don, and Rex walk in to check on Jim, and the Angel—now a nurse who can speak—assures them that she has it "on the highest authority" that Jim will be around for a long time. As Jim awakens, the Angel tells him that she has been granted a leave of absence for good behavior, allowing them to be together. She tells him she is craving French fries, before they embrace and kiss.
