Officers were called shortly after 11.30pm to the junction of Cemetery Lane and Sowerby New Road.
A spokesperson for West Yorkshire Police said: "A 20-year-old man has been arrested in connection with the incident and remains in police custody at this time.
"The victim - a 15-year-old girl - is being supported by specially-trained officers.
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"Enquiries are ongoing by Calderdale Safeguarding Team."
Anyone with information that might help with the investigation should call police via 101 or using the live chat function on the West Yorkshire Police website.