You can do this but it’s going to be a hassle. I had a whole post typed up but I’m not 100% sure about the limitations when using it the way you intend to so I removed it.
So, It looks like to get an Apple Card an iPhone is required? A bit of silly requriement...
I guess an iPad doesn't qualitfy you? Figured that would be enough but guess no. Figure they want people using Apple Pay as much as posssible and not the physical card.
I was able to apply on my iPad, although I was declined! 1st I had to request an invite by tapping Notify Me on their website (https://www.apple.com/apple-card/) The next day, my invite was in my email...with the subject line Get early access to Apple Card. Update to iOS 12.4 to apply. I updated to iOS 12.4 like it stated, and once that was done I went to Settings...Wallet & Apple Pay...Add Card, and Apple Card was there as an option. I applied from there!