Joe L. Allbritton, chairman and chief executive of Riggs National Corp., announced yesterday that he plans to sell his Texas banking interests for $33 million in cash.

A spokesman for Allbritton said the Texas-born financier received a "good price" from Houston's Western Bancorporation Inc. Allbritton said he will sell the two banks owned by his University Bancshares Inc.--University State Bank and First Alief Bank.

On March 31, the banks had combined assets of $207.6 million and deposits of $186.5 million. The price Western was willing to pay for the two banks, the only assets of the privately owned Allbritton enterprise, is more than twice the price put on them last year, before banking and other stocks began a rapid climb in price.

University is not affiliated with other Allbritton holdings--including his ownership of Riggs, as well as his large privately owned holding company, Perpetual Corp. Perpetual owns one bank, Houston Financial Services Ltd. of London, as well as insurance and broadcasting properties.

Two years ago, Allbritton bought controlling interest, about 40 percent, in Riggs. Riggs National Corp.'s only subsidiary is Riggs National Bank, whose $3.7 billion in assets make it the largest commercial bank in the District