They do although they don't necessarily call it that. When I had to get my dad a phone in a hurry from AT&T, the only option was to pay for it monthly as part of my phone bill.
This is better than the old days of getting it 'free' but being locked into a contract that requires you to pay the full cost of the phone if you leave..
All four of the major carriers and Apple offer 0% interest loans on phones.
At least with T-mobile. Even if you have horrible credit as long as you pay your bill on time with them for 12 months, you are eligible for a no interest phone loan.