Is there an option to pay monthly for an iPhone?

Monthly installment payments are an option available in the US to qualified applicants. You can read more about it here:

Apple Card - Monthly Installments - Apple

I was not able to find anything regarding starting with installments then paying in full at a later date. But the Apple Legal page offered this:

For questions about your Installment Loan or your application, please contact Citizens One at 1-888-201-6306.

If you buy through Apple, the only monthly plan available, would be if you have the AppleCard (credit card by Apple).

The best option outside of that would be to buy through your carrier (ATT, Verizon, T-Mobile). That's how I buy all my cellular Apple products (including iPads and AppleWatches).

Read this article about financing options. Availability will depend upon where you live.

Financing and Credit - Apple

As SixFour391 indirectly endorses, the reference I provided you discusses more financing options (carrier offers and Apple Card) than the Recommended reply which only talks about Apple Card.