President Carter will take a week-long work-and-play trip down the Mississippi River on the paddle-wheel steamer Delta Queen, the White House announced yesterday.

Carter, his wife and daughter will ride the riverboat from St. Paul to St. Louis from Aug. 17 to Aug. 24, stopping off at four cities and towns in Wisconsin, Iowa and Missouri.

White House press secretary Jody Powell said the president will use one or more of the stops to plug for congressional passage of his energy program, especially the "windfall profits" tax on oil companies.

But the Carters will remain on board the 188-passenger vessel overnight each night and spend their days relaxing with other tourists who signed up for the regularly scheduled voyage, Powell said.

How much room will be left for others, once White House aides, Secret Service officers and a small group of reporters are accommodated, was not clear.

Powell said the president and Rosalynn Carter will pay the regular fare of about $900 each for the trip (Amy, he said, rides free as a child under 12), and are treating it as part of their summer vacation. Later in August they may visit Camp David or Plains, he said. Last year, the First Family took a trip down Idaho's Salmon River in a rubber raft for a vacation trip.

The schedule for this month's trip calls for the Carters to leave St. Paul on the evening of Aug. 17. They will have opportunities to go ashore in Prairie du Chien, Wis., Davenport and Burlington, Iowa, and Hannibal, Mo., before reaching St. Louis on the morning of Aug. 24.

Powell said the Delta Queen tour is a nonpolitical trip, "since this is not an election year and the president is not a declared candidate." By coincidence, perhaps, Minnesota and Iowa begin their delegate-selection caucuses early in 1980.

Powell said the riverboat trip was suggested to Carter by Sen. Howard H. Baker Jr. (R-Tenn.), an undeclared candidate for the 1980 Republican presidential nomination. Baker and his wife made the trip last year.

Referring to Baker's statement earlier this week that Carter should step aside as a candidate for reelection, Powell said, "Since the president could not respond positively to another of Sen. Baker's suggestions, he decided to accept this one."