Does Toys R' Us accept american express gift cards?

No. Toys “R” US only accepts U.S.-Issued "R" Us Gift Cards.

As stated in their website:

They do not accept the following forms of payment:

CODs
Personal checks
FSA Cards
Gift cards from other merchants

Credit cards accepted by Toysrus.com/Babiesrus.com:

"R"Us credit cards
MasterCard
Visa
American Express
Discover

Other forms of payment that are accepted:

U.S.-Issued "R" Us Gift Cards
PayPal
Cash/Pay in Store

Please note:

Third-party forms of payment and Cash/Pay in Store option ("R"Us Gift Cards & Paypal) cannot be used for all purchases.
Payment may be split between one of the accepted credit cards and a Toys"R"Us or Babies"R"Us Gift Card, but payment can't be split among multiple credit cards.

Before using any gift card be sure to check out Marketplace.com's 7 tips to prevent a gift card nightmare.

In latest buzz, Toys R Us Inc. has filed for bankruptcy reorganization, a victim of the sea change in retailing and the company’s own heavy debt burden, but said it would continue to operate as usual heading into the crucial holiday shopping season.

With its spacious, high-ceiling stores that hold thousands of items, Toys R Us pioneered the big-box format for toy sales and once was the go-to destination for people shopping for toys, baby products and birthday gifts. Read more at Los Angeles Times.

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Tuesday, September 19 2017
Source: https://www.toysrus.com/cobrand/help/payment