Polly Shackleton, the 71-year-old grande dame of District politics who was first appointed to the D.C. City Council in 1967 by President Lyndon Johnson, announced yesterday she is running for a third elected term from Ward 3.

Shackleton, who some observers had expected to retire this year because of her age, was greeted with cheers from a crowd of about 100 persons at the District Building when she boomed, "You're as young as you feel, and let me tell you, I feel great."

Noting she is the same age as President Reagan, Shackleton said, "It's not that I agree with the president's policies--in fact, I don't--but I do feel that if age is no barrier for the presidency , it certainly should not be one to a ward council member."

Shackleton became the first incumbent council member to formally announce for reelection in a year in which the terms of seven of the 13 members are expiring. The major emphasis has been on jockeying for other jobs.

Council members John Wilson (D-Ward 2), Betty Ann Kane (D-At Large) and John Ray (D-At Large) are candidates in the Sept. 14 Democratic mayoral primary. Councilmember Charlene Drew Jarvis (D-Ward 4) also has indicated she is planning a bid for mayor. Of this group of mayoral hopefuls, only Kane, whose term expires this year, is risking her seat on the council.

Council Chairman Arrington Dixon is running for reelection. Council member David A. Clarke (D-Ward 1), is expected to forgo a reelection bid for his current seat and announce within a couple of weeks that he will challenge Dixon. Council member H. R. Crawford (D-Ward 7) also is exploring the chairman's race.

Council members Hilda Mason (Statehood-At Large), Nadine P. Winter (D-Ward 6), and William R. Spaulding (D-Ward 5) are expected to seek reelection, but none has announced so far.

Wilson, Ray, Jarvis, Crawford and Jerry A. Moore Jr. (R-At Large) and Wilhelmina Rolark (D-Ward 8) were elected in 1980 and are in the middle of their four-year terms.

Shackleton, the senior member of the council and chairman of the Human Services Committee which oversees about one-third of the city's nearly $2 billion budget, was endorsed yesterday by Dixon, Mason, Moore, Rolark, Spaulding and Winter.

"I think we are in for some difficult times ahead, and so it is important to have someone with experience and know-how" on the council, said Shackleton, who was first elected in 1974 and reelected in 1978 to represent the affluent, predominantly white ward lying west of Rock Creek Park.

An unknown factor in the race this year is the effect of redistricting, which placed most of the Georgetown area in Ward 2. Only a small sliver of Georgetown, including Shackleton's home, was left in Ward 3.

Shackleton is being challenged in the Democratic primary by Ruth Dixon, former president of the D. C. League of Women Voters, and Mark Plotkin, an attorney. Kay McGrath, an official of the city's Office of Planning and Development who was actively considering a bid for Shackleton's seat, has dropped out of the race in support of Shackleton.

Carol Schwartz, a former member of the school board from Ward 3 who did not seek reelection last year, is also considering the council race. Schwartz is a Republican, and thus would not face Shackleton and the others in the Democratic contest.