The Housing and Urban Development Department handed out the first of its long-delayed housing vouchers at a ceremony yesterday in San Antonio. The first recipient under the program, which Congress approved in 1983, was Estella Sanchez, a 34-year-old mother of four.

HUD has said the program will give aid recipients more choice in their housing and noted that with the voucher, Sanchez would qualify for a three-bedroom house anywhere in San Antonio.

The voucher would make up the difference between what the family could pay and their rent, up to what HUD figures is the fair market rent in the area -- $472 in the case of a three-bedroom house in San Antonio. The family would save money if it found a cheaper place, but would pay more if it took a more expensive one.

The department had announced last summer the areas it had chosen to participate in the program -- which is a demonstration -- but wascriticized when it turned out months later that it had not actually gotten the money out to local officials.

HUD Secretary Samuel R. Pierce Jr. had promised the House housing subcommittee that he would have vouchers in the hands of recipients before the end of April.