Nortje, 30, has not played a T20 international for more than a year due to persistent injuries, and on his return in the Indian Premier League this season he has given up a woefully high 13.36 runs per over across six matches.
Batter Rickelton, who can also keep wicket, has been rewarded for his fine form in SA20 this year, in which he was the leading scorer with 530 runs at an average of 58.88, while seamer Baartman took 18 wickets in eight matches in the competition.
Aiden Markram will captain the squad, which also includes power hitters Heinrich Klaasen, David Miller, Quinton de Kock and Tristan Stubbs.
South Africa have elected to take three frontline spinners in Bjorn Fortuin, Keshav Maharaj and Tabraiz Shamsi, with Markram a useful slow bowling option.
"Selecting this group was extremely tough considering the amount of T20 cricket that has been played recently and the form that has been on show," South Africa's white-ball coach Rob Walter said on Tuesday.
South Africa, who have never won a World Cup in either the 50- or 20-over format, will prepare for the tournament with a three-match T20 series in the West Indies.
They have Bangladesh, Netherlands, Nepal and Sri Lanka in their group at the World Cup, opening their campaign against the latter in New York on June 3.
Jointly hosted in the United States and the West Indies, the World Cup runs from June 2-30 (AEST).
SOUTH AFRICA SQUAD
Aiden Markram (capt), Ottniel Baartman, Gerald Coetzee, Quinton de Kock, Bjorn Fortuin, Reeza Hendricks, Marco Jansen, Heinrich Klaasen, Keshav Maharaj, David Miller, Anrich Nortje, Kagiso Rabada, Ryan Rickelton, Tabraiz Shamsi,Tristan Stubbs.
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