I can’t find the option to apply for the Apple Card on my device

The option to apply for an Apple Card is inside the Add new card to Apple Pay option seen as the (+) sign in the top right corner of the Wallet App.

If you don't see the (+) sign, your iPhone's region is not set to a country where Apple Pay is available.

If you do see it, but there is no Apple Card option in the Card Type screen, then your iPhone's region is not set to the U.S. most likely.

Apple Card is only available in the U.S at this time.

The following has a list of requirements that may explain or help: How to apply for Apple Card - Apple Support

Are you in the US?

Are you sure Settings->General->Language & Region->Region is set to the U.S.?

So you are physically in the US?