Rep. John B. Anderson said today he had retained New York political consultant David Garth to explore whether it would be practical for Anderson to seek the presidency as an independent candidate.

The Illinois congressman, who has been running for the Republican presidential nomination, said he asked Garth to survey the "legal technicalities and overall political feasibility" of an independent candidacy. t

He said no time table had been set for Garth to report or for Anderson's decision.

Garth is a veteran political strategist and television campaign commercial producer, who has worked for prominent candidates of both parties in past mayoral, gubernatorial, senatorial and presidential campaigns.

Anderson said he had taken the step because "I have been besieged with so many requests to consider seriously running as an independent candidate . . . that I could not in conscience ignore them."

He disclosed his Thursday meeting with Garth in New York in an interview this morning on the NBC "Today" show, and amplified his comments in a speech and press conference at the University of Pennsylvania.

Anderson emphasized that while he has retained Garth as an adviser on the independent candidacy the New Yorker was working "without pay and on a noncontractual basis."

If Anderson were spending money to explore an independent candidacy, he might jeopardize the federal matching funds he is now receiving to help his campaign for the GOP nomination.

Nonetheless, his decision to seek out Garth and authorize him to explore the possibility of an independent race was seen by political observers as a significant step toward such a candidacy. Anderson has attracted a national following but has yet to win a Republican primary. Garth's reputation among political insiders would probably attract money and support for such a bid.

Anderson came here to raise funds for his present campaign and to encourage write-in votes in the April 22 Pennsylvania Republican primary, where his backers failed to collect enough signatures to place his name on the ballot.

He said he believed there was "a feeling of growing disenchatment" among voters at the prospect of a general election campaign between President Carter and Ronald Reagan. "But I would like to have my feeling reinforced" by Garth's survey before making the decision, he said.