You can certainly apply for a Disney Premier Visa Card when you arrive at the Disneyland Resort!
I will tell you, however, that it's unlikely you'll actually receive the card while you're there.
Further, merchandise locations may not accept the approval letter as a form of payment so you're better off applying online and if you don't receive the card in time for your upcoming trip, at least you'll be able to start accumulating Disney Rewards Dollars as soon as you return home!
I know of at least two locations where you can apply for a Disney Visa in person. One is in the Downtown Disney District. The other is at the Disneyland Resort Hotel.
Most importantly, you can stop by any Chase Bank near Disneyland and request a Disney Visa application.
Have a Magical Time at the Disneyland Resort!
On 9/7/2017 Trinity from TX Asked: Hi! Disneyland used to have a ONE HOUR shopping pass? We used to leave our DL and Credit Card at guest services and could go shop for a very limited time. Does this still exist?