D.C. City Council member John A. Wilson, whose name has darted in and out of the running as a candidate for mayor or City Council chairman, yesterday put himself back in the running as a possible candidate for chairman by obtaning documents he would need to complete in order to qualify for the Sept. 12 Democratic primary.

Wilson, the 34-year-old Democrat from Ward 2, was quick to say that he still isn't sure if he will run. "I'm not a candidate for anything at the present time," he said in a telephone interview.

Instead, Wilson said, he is yielding to pressure from persons - none of whom he would name - to draft him. "I think people want another choice," he said, "and it seems like I am that choice."

"A lot of people have been hassling me about running. A lot of people have been saying I am shirking my responsibility by not running," Wilson said. "There are people telling me they want me to run for chairman, and I am giving them the opportunity to show me what they can do.

"I've told them, 'if you can show me 2,000 people to sign my petitions, the documents which he picked up yesterday, then I will seriously consider entering the race."

The two major candidates for chairman in the Democratic primary at this point are two of Wilson's Council colleages - Arrington Dixon (D-Ward 4) and Douglas E. Moore (D-At Large).

A recent poll by The Washington Post showed Dixon a more than 2 to 1 favorite over Moore among Democratic voters, and Wilson's entry into the race would be likely to split the vote for Dixon, according to several city political observers.

Wilson, who is closer politically to Dixon than to Moore, said in characteristic nonchalant fashion yesterday, "I'm not interested in dividing the Dixon vote or the Moore vote. I'm interested in winning. Maybe I'll split both their votes and win."

When asked if he had discussed hi-entry into the race with any other candidates or leading city politicians, Wilson responded, "Why should I? They didn't talk to me.

Asked who was supporting him and who could circulate the petitions, Wilson said, "I don't want to talk about it."

Several months ago, Wilson, whose council term expires in 1980, had publicly ruled himself out of running for anything. But yesterday he said, "I've seen the candidates. I've heard them. I've seen the polls. I've seen other people's polls that say I have a better name recognition than those in the race. One has to adapt to ever-changing political events."

Moore said he would welcome Wilson into the race. "However, I don't think he's serious," he said.

Dixon said he was not sure how serious Wilson was either, and added that Wilson's plans would not affect his own.

The third announced candidate in the race is the Rev. John G. Martin, pastor of Holy Conforter Baptist Church.