Federal Trade Commissioner Paul Rand Dixon called consumer advocate Ralph Nader "a son of a bitch" and "a dirty Arab" during a Jan. 17 speech before a trade industry association, according to members of the audience.

Dixon would not deny yesterday that he made the ethnic slur, but he said he could not recall his remarks because he had no written record.He said he had referred to Nader as "a son of a bitch as far as his relations with me."

In 1969 Nader, who is of Lebanese descent, brought out a book critical of the Federal Trade Commission and Dixon's role as chairman. Dixon, 63, has served as a member of the Federal Trade Commission since the early 1960s and was the chairman of that consumer protection agency for several years.

Dixon made his remarks about Nader before about 50 people attending a conference in Arlington of the Grocery Manufacturers of America Inc. One member of the audience, a man of Arab descent, took notes during Dixon's talk on the topic of the relationship between trade associations and regulatory agencies. The man later wrote a letter to Dixon to protest his deprecation of Arabs.

Dixon apologized to the man by telephone last month and told a reporter yesterday, "If I said anything like that it was a mistake. There may be a hell of a lot of good Arabs who might (take offense) if you called them a dirty so-and-so, so I have no intention of saying that about anybody."

Informed of Dixon's remarks yesterday, Nader demanded an apology "not just to me, but to many people and to President Carter because tht kind of bigotry should be offensive to everyone."

Dixon said he did not intend to apologize to Nader, who Dixon said "has taken pretty good license with me."

The National Association of Arab Americans said it intends to deliver a protest of Dixon's remarks to the White House today.