Short answer: No. But let’s look at a few specifics where you may be asked to pay.
First, there are companies that represent themselves as mystery shopping companies that can award shops, and they charge shoppers a membership fee or other charge to access available assignments. These are not mystery shopping companies. Mystery shopping companies do not charge you to apply. Never pay to apply, and never pay a “membership fee” to get mystery shopper jobs.
You do not need to pay to view available assignments. Sign up with as many mystery shopping companies as you can, and you will have more shop notices than you can handle. I have a list of 200 legitimate companies (none of them will charge you) here at MysteryShoppersManual.com. There are also job boards, such as Jobslinger.com, where you can view postings from many mystery shopping companies.