Several offensive songs were heard from the section of Shielfield Park housing travelling supporters at the Third Division match, which was broadcast live on television.
Northumbria Police said there had been two arrests.
Rangers issued an apology while the match was still going on after microphones placed by broadcaster ESPN picked up the offensive chants.
TV presenter Ray Stubbs said the broadcaster was contacting the police over the issue.
It is understood the Ibrox club will assist any police inquiry into criminal acts and the club will ban those responsible from all Rangers matches.
A Rangers' spokesman said: "The club is disappointed by certain outbursts of inappropriate singing by a section of the support at Berwick."
Northumbria Police said it was reviewing footage of the match.
Officers also said legislation covering sectarian chanting applied to travelling fans and was enactable outside Scotland.
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