The Light Blues are featuring at this stage of the competition for the first tiime in 41 years and the match is scheduled for September 29.
It will be the first time at Mosset Park for Rangers who only previously played Forres once, winning 6-0 in a friendly at Ibrox in 1908.
Forres are the reigning Highland League champions, having gone 26 years since their previous success.
There is a possibility that the tie will be switched to a larger venue as Mosset Park only has a capacity of 1400, most of that standing.
Secretary David Macdonald saiid: "We are absolutely delighted to have drawn Rangers in the Cup - it's going to be fantastic for everyone connected with the club.
"We had a chance of facing Rangers in 2009. The winners of our tie with Forfar were due to meet Rangers but unfortunately we lost out that time.
"It's only just sinking in. We have a committee meeting planned for tomorrow night so we will be able to discuss everything about the tie."
DRAW IN FULL
1. Cove Rangers v Golspie Sutherland
2. Fraserburgh v East Stirlingshire
3. Forres Mechanics v Rangers
4. Clachnacuddin v Formartine United
5. Civil Service Strollers v Turriff United
6. Montrose v Shotts Bon Accord or Edinburgh City
7. Buckie Thistle or Rothes v Annan Athletic
8. Berwick Rangers v Wick Academy
9. Selkirk v Vale of Leithen
10. Inverurie Loco Works v Huntly or Wigtown & Bladnoch
11. Deveronvale v Peterhead
12. Elgin City v St Cuthbert Wanderers
13. Dalbeattie Star v Stirling Albion
14. Queen's Park v Irvine Meadow
15. Stirling University v Bonnyrigg Rose
16. Clyde v Nairn County