The D.C. City Council, which earlier this year voted itself the right to decide what type of cable television franchises can be awarded in the District, is moving slowly in appointing members to its advisory cable design commission.

Though the measure that set up the commission became law Aug. 8, only 10 of the council's total of 21 available appointments had been submitted by Monday.

Council member Wilhelmina J. Rolark (D-Ward 8), chairman of the Committee on Public Service and Consumer Affairs that is overseeing formation of the cable commission, sent a memo a month ago to council members urging them to appoint commission members as quickly as possible.

The District is several stages -- and possibly years -- behind other area jurisdictions in making the politically sensitive decision to award what is expected to be a lucrative contract for the winning firm. City officials have said that, at best, cable will not be available in the District for two years.

Mayor Marion S. Barry, who unsuccessfully tried to persuade the council to give him the power to award cable franchises, will name seven additional persons to the commission. Under the law, however, his appointments cannot be made until after the council completes its selection process. In addition, Barry's appointees are limited to those that will "balance" the commission in terms of consumer and minority groups.

Once the commission is established, it will have 90 days to recommend what type of system the city should develop and the conditions private cable firms will have to follow to submit bids. The first formal meeting of the commission is not expected until December, council officials said.

Besides the lag in appointments, funding for the proposed commission, initially set at $40,000, expired Sept. 30 when the 1982 fiscal year ended. Before the commission can hire consultants or staff, the council will have to find a new source of money.

After Rolark circulated her memo last month, she appointed William P. Lightfoot, a personal injury attorney here, chairman of the 28-member commission. Lightfoot, Rolark's former chief staff clerk, was the principal staff member who helped draft the cable television legislation.

Each of the eight council members who chair the council's standing committees can appoint two members to the commission. The other five members of the council were given one appointment to make. The appointments are for one year and the members serve without compensation except for expenses.

In addition to Lightfoot, who also is president of the Bloomingdale Civic Association and the former head of Rolark's Ad Hoc Committee on Cable Television, Rolark also appointed Deputy U.S. Marshal Donald L. Smith to serve on the commission.

Other members appointed by council members include Tayloe Ross and Donald L. Nunley, who were appointed by John A. Wilson (D-Ward 2). Ross is a longtime advocate for more participation by women and minorities in the media and Nunley, a former official of Friendship House Inc., is a former teacher and counselor.

Council member William R. Spaulding (D-Ward 5) named Frederick A. Smith, a retired school principal and Dr. Clarence E. Wade.

Polly Shackleton (D-Ward 3) chose Marjorie Newman, a real estate marketing official who has been active in promoting broadcasting opportunities for women and minorities, and Bruce D. Jacobs, a staff attorney for the National Citizens Committee for Broadcasting, a research firm.

Nadine P. Winter (D-Ward 6), named L. Leonard Hacker, president of LAND, a real estate syndicate.

H.R. Crawford (D-Ward 7) appointed Charles Dorsey, a member of his staff.

Charlene Drew Jarvis (D-Ward 4), named Jerome Shuman, a professor of law who specializes in franchising and regulated industries at Howard University Law School, and Woodrow Boggs Jr., an attorney and a chief adviser to Jarvis.

The members who had not sent their appointments to Rolark by Monday included Hilda Mason (Statehood-At Large), David A. Clarke (D-Ward 1), and Jerry A. Moore (R-At Large), all of whom can make two appointments, and Betty Ann Kane (D-At Large), who has one appointment.

Rolark's staff also said appointments had not been received from Council Chairman Arrington Dixon and John Ray (D-At Large), although the names of their appointments were released Monday.

Dixon's staff said he would appoint Darlene Palmer, a telecommunications aide in former president Carter's administration, and Winfield Scott, associate dean of the George Washington University's medical school and a gay political activist.

Ray's staff said he would appoint James Baldwin, a former director of the Office of Human Rights and a member of the D.C. Statehood Constitution Convention, who was the Ward 7 coordinator for Ray's recent mayoral bid.