The Midlothian based side currently sit top of the Lowland League and, like the Broch, are unbeaten so far this season having won six and drawn one of their seven matches.
Managed by former Berwick Rangers boss Robbie Horn, the Rose are competing in their first season in the Lowland League after gaining promotion as East of Scotland champions last season.
The match is due to take place on Saturday, September 21.
The full Scottish Cup first round draw as follows: Broxburn Athletic v East Stirlingshire, Buckie Thistle v Civil Service Strollers, Caledonian Braves v Rothes, Cumbernauld Colts v Penicuik Athletic, Dalbeattie Star v Gala Fairydean Rovers, Edinburgh University v Lochee United, Forres Mechanics v Banks O’Dee, Fort William v Vale of Leithen, Fraserburgh v Bonnyrigg Rose Athletic, Gretna 2008 v Hill of Beath Hawthorn, Inverurie Loco Works v Wick Academy, Jeanfield/Linlithgow v Huntly, Keith v University of Stirling, Kelty Hearts v Auchinleck Talbot, Nairn County v Clachnacuddin, Spartans v Deveronvale, Strathspey Thistle v Lossiemouth and Turriff United v Formartine United.
In other cup news, Fraserburgh were in action on Wednesday night (after the Fraserbrugh Herald had gone to print) as they travelled to Buckie Thistle in the semi-final of the Aberdeenshire Cup.
A win for Mark Cowie’s side would set up a final encounter with Formartine United at Cove Ranger’s Balmoral Stadium on Friday, September 11.
This Saturday the Broch’s attention remains on league duties as Forres Mechanics are the visitors to Bellslea Park.
The other HFL matches are: Clach v Buckie, Formartine v Fort William, Huntly v Locos, Lossiemuth v Keith, Nairn v Strathspey, Rothes v Vale and Wick v Turriff.