The accused was identified as Manik Mia, 24, a cousin of the victim’s friend.
Officer-in-Charge of Kotwali Police Station Moniruzzaman said the victim went to a friend's house on Oct 22 where Manik offered to marry her.
Manik and his parents took the girl to a local office where they staged a fake marriage and secured the victim's signature.
On Oct 24, the victim fell sick after being repeatedly raped by Manik. He also beat up the girl and abandoned her, denied that he married her.
Later, a private organisation - Jashore Justice and Care - rescued the girl and informed police.
The victim filed a case on Monday night.
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