AT&T Inc. is raising prices by as much as 33% for the data plans sold with its smartphones and tablet computers.

The Dallas-based carrier said that effective Jan. 22, new customers on its least-expensive smartphone plan will pay $20 a month for 300 megabytes of data, compared with the current 200-megabyte plan at $15. Smartphone or tablet users needing more data will need to pay $30 for a 3 gigabyte plan, up from $25 for 2 gigabytes.

"Data...