Culter, from Aberdeen, are the Northern Superleague champions, and the first ever meeting between the two sides will be held on the weekend of November 2/3.
Berwick also face more northern raiders this weekend when they take on Elgin at Shielfield in the league.
Like Rangers, City enjoyed a win in the second round of the Scottish Cup last weekend - whilst Berwick were beating Peterhead 2-1, they were winning 4-0 away at Keith.
There is very little between the two sides - they are currently separated by only two points in the SPFL 2 table, and another tough match is in prospect.
But Berwick assistant manager Robbie Horn believes his side ‘put down a marker’ for the league with their win over the Blue Toon at the weekend.
“Peterhead are a good side,” said Horn, “but we showed with our performance and result against them that we were better than them on the day.
“We are also a good side. We have made a decent start to our league campaign, now it’s all about maintaining that form and pushing on between now and Christmas.
“Our home form so far this season has been very good, and with home games coming up against Elgin, Clyde and Montrose in three of the next four weeks, we have to go into these matches with some confidence.”
Berwick will welcome back goalkeeper Paul Grant and skipper Lee Currie for the visit of Elgin.
Both missed the cup win over Peterhead - Grant was unavailable as parent club Hibernian did not want to risk him being cup-tied in case they have to recall him later in the season, whilst Currie had a suspension carried over from last season’s competition.
Billy Bald was called up for his first team debut, and he did not let the team down, pulling off a fine one-handed save from close range in the second half, which kept Rangers in the game.
“Billy is an experienced keeper,” said Horn, “and he did very well for us. The situation with Paul is unfortunate, but it is not of our making.”
Manager Ian Little said the unavailability of players, plus the fact that two others (Dougie Brydon and Owen Ronald) are currently out injured, stresses the need for a squad.
“We had to bring players in for the Peterhead game,” he said, “but they stepped up to the plate and I was delighted with the fighting qualities shown by everyone.
“If we could win every game by coming from behind with a performance like that I would be happy, but of course that is not always possible.”