A new credit-card concept would allow cardholders to pay and build credit on their largest monthly expense: rent.

Bilt Technologies Inc., a real-estate startup, is joining with Evolve Bank & Trust and Mastercard Inc. to launch a credit card designed for renters. Users can accumulate rewards points through rent and other spending, with no fees charged to the tenant or the landlord when paying rent on the card, according to Bilt.

Rewards points can then be put toward rent and other purchases, even toward a down payment on a house. “We believe paying rent should build your credit score because it’s your single largest liability,” said Ankur Jain, founder of Bilt.

Many landlords already accept credit cards, but they typically pass on processing fees to renters, often totaling about 3%. For landlords that don’t accept plastic, Bilt says it will mail landlords paper checks on behalf of the tenant, then charge the renter’s credit-card account, with no fee.

The partnership can afford to offer no-fee rent payments because of the fees that Evolve and Mastercard will collect from all other types of spending on the card, according to Bilt. The card program also attempts to incentivize non-rent spending by increasing the rewards for rent when cardholders spend more on everything else. Mastercard declined to elaborate further on how it will profit from the card without fees on rent payments.

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Unlike homeowners, who build equity with every monthly mortgage payment, renters get no long-term benefits from their monthly payments. Paying by credit card gives renters some additional value that could help them buy a house, Bilt says.

Cards do this partly by improving renters’ credit scores. The Bilt cards, set to launch Tuesday, also do this because points can be used for a down payment.

When a card user goes to buy a home, Bilt says it will convert rewards points into cash and deposit the money into the home-sale escrow account. “It should be a path to homeownership,” said Mr. Jain.

Still, it would take a lot of rent money and time to build enough points to put a dent in a down payment. For the typical card user spending $1,500 on monthly rent for 10 years, Bilt estimates the accumulated points savings for a down payment would equal about $6,000.

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In recent years, financial-technology companies have come up with more ways to allow renters to either finance rent payments or put them on credit cards.

But credit counselors often warn against using credit to pay rent, because many cards come with high interest rates and because rent is typically such a large expense. The average annual percentage rate on the Bilt card, for example, will run between 15% and 22.5%. The highest rate for subprime cardholders will top out at 30%.

Bilt hopes to avoid letting the card become a debt trap through a tool that disables rent payments when users don’t have sufficient cash savings in a linked bank account. Card users deemed higher risk will be required to use the feature. For other users, rent still has to be paid off within one month and no interest will be collected on rent spending, according to Bilt.

Home prices have rallied during the pandemic, and the relative shortage of homes available to buy has produced the tightest housing market in many years.

The median sales price of a U.S. home that was financed with a mortgage was $306,500 during the first quarter of 2021, according to real-estate data provider Attom Data Solutions. The median down payment was $18,700. The median age of a first-time home buyer was 33 years old, according to a 2020 report from the National Association of Realtors. In the hot housing market, more buyers with small down payments are seeing their offers rejected in favor of competitors who can put more money down.

The Bilt card will allow rent payments to be made to any landlord, but several large apartment operators also plan to accept the card payments as part of existing loyalty programs.

These landlords include AvalonBay Communities, a publicly traded company that owns nearly 80,000 apartment units. Karen Hollinger, a senior vice president with AvalonBay, said that such rewards and loyalty programs are common in the hotel industry and are now being used by apartment owners as tenant-retention and marketing tools.

Write to Will Parker at will.parker@wsj.com