Wireless carriers have long made smartphones look cheaper to consumers by subsidizing their cost. Now Apple Inc. is trying to woo phone buyers, offsetting the price of devices with generous trade-in offers.

The company has rolled out at least one new iPhone in each of the last several years, adding features that have pushed the starting price of its top-of-line model above $1,000. With less fanfare, Apple has also let U.S. customers trade in older models for credit—a program it is now hoping will help mitigate the sticker...