President Carter announced yesterday he will nominate Reubin Askew, former governor of Florida, to be his special trade representative, replacing Robert S. Strauss, who is now special ambassador to the Middle East peace talks.

The appointment was seen as aimed at bolstering Carter's political standing in the South in advance of the 1980 election. Askew has little hard experience in trade matters, and there are no major trade issues expected in coming months.

Askew, now 50, was among a small group of Southern governors - including Carter - who were regarded in the early 1970s as symbolic of the "New South." Askew once headed a trade committee of the National Governors Association.

The White House said Alonzo L. McDonald, who has served as Strauss' deputy since 1977, would be acting special trade representative until Askew's nomination is confirmed by the Senate, possibly around October 1.

Askew has been telling inquirers in recent months that he was looking for a high-level government post that would groom him for a role as an elder statesman and troubleshooter on foreign policy issues.

He specifically cited Averill Harriman, the former New York governor, as a model. Although nominally a private citizen, Harriman, also a former governor, has been drafted from time to time for special assignments, such as Vietnam peace negotiator.

Jody Powell, Carter's press secretary, said yesterday the president had "long admired" Askew's abilities during his years as governor. Powell said the trade negotiator's job would continue to be a cabinet-level post.

The appointment comes at the end of a major overhaul of the world trade system, which essentially has completed negotiations on most significant trade issues. The pact, negotiated by Strauss, was approved by Congress last month.

Askew met with Carter and Strauss on Tuesday and stayed at the White House Tuesday night before returning to Miami, where he is a lawyer specializing in international corporate law.

A native of Muskogee, Okla., Askew served as a county prosecutor and later a state legislator in Florida before winning election as governor in 1970. He served as the state's chief executive until 1979.

McDonald, a native of Atlanta, was head of the U.S. delegation in Geneva that conducted day-to-day negotiations in the recent trade talks. He formerly was a consultant with McKinsey and Company, which has offices worldwide. CAPTION: Picture, Former Florida Gov. Reubin Askew talks with President Carter before being named to succeed Robert Strauss. AP