Can I bring a pack of razor blades on a plane?

In the US, you can bring safety razor blades in checked luggage only. It does not matter whether they're in any particular kind of pack; they are prohibited in the cabin because of the danger that someone might use one as a weapon.

Hilmar helpfully provided a source in a comment: https://www.tsa.gov/blog/2010/08/17/safety-razors-and-disposable-razors

Note that the rules governing air security vary from one country to another. As you've said you're traveling to the US, you will be boarding in another country. You should check that country's rules to see whether you can bring the blades in your checked luggage.

In the EU, razor blades like this are also not permitted in hand luggage, according to the official website of the European Commission:

c. objects with a sharp point or sharp edge (capable of being used to cause serious injury), including: … - razor blades, …

It's easy to imagine you can turn a couple of such blades into a dangerous weapon using a simple holder.

Personally, I'd suggest packing a few disposable cartridge razors if you don't check in your luggage and only fly for a few days. For longer trips I'd just buy a pack of DE razors at the destination.