HOUSTON (AP) _ A mayoral candidate who said during a live, televised interview that the way to control AIDS was to ''to shoot the queers'' raised $69,105 in one day after making the comment, financial records indicate.

Louie Welch later apologized for the ''unfortunate remark,'' broadcast Oct. 24 when a technician accidentally turned up the candidate's microphone. But Welch said he was in good company, pointing to President Reagan's well- publicized comment during a microphone test about bombing Russia.

Welch campaign treasurer James Franklin said the faux pas had provided a ''burst of energy and activity'' to fund-raising efforts.

''The truth is getting out to people,'' Franklin said.

According to campaign finance reports filed Tuesday, Welch has raised about $1.5 million since he entered the race, including $678,000 in the 30-day period that ended Friday. Contributions totaled $69,105 last Friday alone, the day after Welch made the remark.

Welch will face incumbent Mayor Kathy Whitmire in the Nov. 5 election. Mrs. Whitmire, 39, reported contributions of almost $1.4 million, records showed.

Mrs. Whitmire raised about $350,000 in contributions in the 30-day period that ended Friday.

Sheila Rushlo, a mayoral spokeswoman, said specific figures for Friday's contributions were not available.

Welch, 66, is a former five-term mayor who recently introduced the prevention of acquired immune deficiency syndrome as a campaign issue in the race. AIDS is an affliction in which the body's immune system becomes unable to resist disease.

Mrs. Whitmire is seeking her third term, and received the support of the homosexual community in her previous bids.

Local gay political leaders said they were not amused by Welch's comment.

''It's a sick joke - if it's a joke,'' said Sue Lovell, president of Houston's Gay Political Caucus.