The world-famous chain is looking to fill a range of posts including managers, bar workers, cooks and hosts for the latest restaurant in the company's empire.
And within a day of the jobs being announced earlier this week, more than 4,000 hopefuls had been in touch.
The venue, at the former Athenaeum Theatre in Buchanan Street, opens in November and will seat 170.
Rock memorabilia on show will include a suit worn by The Who's Pete Townsend in the movie Tommy.
The new recruits will join a workforce of 39,000 in Hard Rock venues in more than 50 countries. Director of European Human Resources Debbie Galbraith said: "We are absolutely overwhelmed by the response."